Arshad Habib, A. H. Malik, A. Memon, Feroza Arshad, Mehwish Shaikh
The novel fractional order intelligent transient dynamics and advanced fractional order nonlinear robust control synthesis scheme of the Pressurized Water Reactor (PWR) pressurizer are addressed in this research work. The Graphical User Interface (GUI) is designed for closed-loop model-based PWR pressurizer dynamical studies in LabVIEW. Based on the demand for power, the reactor power and turbine power are predicted using a fractional order backpropagation algorithm in an open loop configuration. Using turbine power and heater power as input variables, pressurizer level, pressurizer pressure and coolant average temperature as output variables, the open loop multi-input multi-output (MIMO) dynamic model of pressurizer is estimated using fractional order artificial intelligence in LabVIEW. Four fractional order robust nonlinear H∞ sub-controllers are designed for charging flow, spray flow, proportional heaters power and backup heaters power. All the dynamic controller models are in fractional order nonlinear H∞ framework and are designed in LabVIEW. The performance of the proposed design work is evaluated in closed loop configuration at 100 %, 75 % and 15 % in steady state conditions. Dynamic transient analysis is performed from 100% to 90% power reduction scenario and found satisfactory and within design limits and robust bounds.
{"title":"Fractional Order Modeling of PWR Pressurizer Dynamics and Fractional Order Nonlinear H∞ Controllers Design in LabVIEW","authors":"Arshad Habib, A. H. Malik, A. Memon, Feroza Arshad, Mehwish Shaikh","doi":"10.53560/ppasa(59-3)778","DOIUrl":"https://doi.org/10.53560/ppasa(59-3)778","url":null,"abstract":"The novel fractional order intelligent transient dynamics and advanced fractional order nonlinear robust control synthesis scheme of the Pressurized Water Reactor (PWR) pressurizer are addressed in this research work. The Graphical User Interface (GUI) is designed for closed-loop model-based PWR pressurizer dynamical studies in LabVIEW. Based on the demand for power, the reactor power and turbine power are predicted using a fractional order backpropagation algorithm in an open loop configuration. Using turbine power and heater power as input variables, pressurizer level, pressurizer pressure and coolant average temperature as output variables, the open loop multi-input multi-output (MIMO) dynamic model of pressurizer is estimated using fractional order artificial intelligence in LabVIEW. Four fractional order robust nonlinear H∞ sub-controllers are designed for charging flow, spray flow, proportional heaters power and backup heaters power. All the dynamic controller models are in fractional order nonlinear H∞ framework and are designed in LabVIEW. The performance of the proposed design work is evaluated in closed loop configuration at 100 %, 75 % and 15 % in steady state conditions. Dynamic transient analysis is performed from 100% to 90% power reduction scenario and found satisfactory and within design limits and robust bounds.","PeriodicalId":36961,"journal":{"name":"Proceedings of the Pakistan Academy of Sciences: Part A","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48004630","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Z. Kalhoro, Zubair Zaheer Ahmed, Ahmed Kalhoro, Abdul Wasim Shaikh, Muhammad Shakeel, Rind Baloch, Owais Ali Rajput
To solve the system of linear equations is one of the hottest topics in iterative methods. The system of linear equations occurs in business, engineering, social and in sensitive research areas like medicine, therefore applying efficient matrix solvers to such systems is crucial. In this paper, an improved iterative scheme using successive overrelaxation has been constructed. The proposed iterative method converges well when a linear system’s matrix is M-matrix, Symmetric positive definite with some conditions, irreducibly diagonally dominant, strictly diagonally dominant, and H-matrix. Such type of linear system of equations does arise usually from ordinary differential equations and partial differential equations. The improved iterative scheme has decreased spectral radius, improved stability and reduced the number of iterations. To show the effectiveness of the improved scheme, it is compared with the refinement of generalized successive over-relaxation and generalized successive over-relaxation method with the help of numerical experiments using MATLAB software.
{"title":"An Improved Iterative Scheme using Successive Over-relaxation for Solution of Linear System of Equations","authors":"Z. Kalhoro, Zubair Zaheer Ahmed, Ahmed Kalhoro, Abdul Wasim Shaikh, Muhammad Shakeel, Rind Baloch, Owais Ali Rajput","doi":"10.53560/ppasa(59-3)653","DOIUrl":"https://doi.org/10.53560/ppasa(59-3)653","url":null,"abstract":"To solve the system of linear equations is one of the hottest topics in iterative methods. The system of linear equations occurs in business, engineering, social and in sensitive research areas like medicine, therefore applying efficient matrix solvers to such systems is crucial. In this paper, an improved iterative scheme using successive overrelaxation has been constructed. The proposed iterative method converges well when a linear system’s matrix is M-matrix, Symmetric positive definite with some conditions, irreducibly diagonally dominant, strictly diagonally dominant, and H-matrix. Such type of linear system of equations does arise usually from ordinary differential equations and partial differential equations. The improved iterative scheme has decreased spectral radius, improved stability and reduced the number of iterations. To show the effectiveness of the improved scheme, it is compared with the refinement of generalized successive over-relaxation and generalized successive over-relaxation method with the help of numerical experiments using MATLAB software.","PeriodicalId":36961,"journal":{"name":"Proceedings of the Pakistan Academy of Sciences: Part A","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47012367","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
One of the technologies that are now expanding rapidly is called the Internet of Things (IoT). It is a technology that enables billions of smart devices or things, collectively referred to as “Things,” to collect a variety of data about themselves and the environment in which they are located using a variety of sensors. They can then share data with parties who have been permitted to do so for a variety of objectives, such as the management and monitoring of industrial services or the expansion of company services or operations. However, there are presently more security risks associated with the Internet of Things than ever. The field of machine learning (ML) has recently experienced significant advancement in technology, which has resulted in the opening of various new lines of inquiry that may be used to address existing and upcoming issues related to the Internet of Things. Nevertheless, machine learning is a robust technology that can recognize suspicious dangers and activities in smart devices and grids. The authors of this paper conducted an extensive literature review on Machine Learning methods and the significance of IoT security in the context of various types of potential attacks. After that, they compared several different ML algorithms regarding the detection of attacks and anomalies. Additionally, many machines learning-based Internet of Things protection systems have been presented.
{"title":"Machine Learning Methods of IoT Security and Future Application","authors":"Aqib Ali, Samreen Naeem, Sania Anam, M. Ahmed","doi":"10.53560/ppasa(59-3)782","DOIUrl":"https://doi.org/10.53560/ppasa(59-3)782","url":null,"abstract":"One of the technologies that are now expanding rapidly is called the Internet of Things (IoT). It is a technology that enables billions of smart devices or things, collectively referred to as “Things,” to collect a variety of data about themselves and the environment in which they are located using a variety of sensors. They can then share data with parties who have been permitted to do so for a variety of objectives, such as the management and monitoring of industrial services or the expansion of company services or operations. However, there are presently more security risks associated with the Internet of Things than ever. The field of machine learning (ML) has recently experienced significant advancement in technology, which has resulted in the opening of various new lines of inquiry that may be used to address existing and upcoming issues related to the Internet of Things. Nevertheless, machine learning is a robust technology that can recognize suspicious dangers and activities in smart devices and grids. The authors of this paper conducted an extensive literature review on Machine Learning methods and the significance of IoT security in the context of various types of potential attacks. After that, they compared several different ML algorithms regarding the detection of attacks and anomalies. Additionally, many machines learning-based Internet of Things protection systems have been presented.","PeriodicalId":36961,"journal":{"name":"Proceedings of the Pakistan Academy of Sciences: Part A","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-08-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42622691","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We have studied the Laplacian equation in non-integer space which had been previously used to describe complex phenomena in physics and electromagnetism. We have applied this idea to a dielectric cylindrical shell to find the electric potential and field of a dielectric coated cylinder analytically in fractional dimensional space. The problem is derived using Gegenbauer polynomials. This close form gneral solution solved in fractional dimensional space can be applied for various materials of cylindrical shell, outside shell and inside the cylindrical core. The obtained solution is retrieved for integer order by setting the fractional parameter α=3.
{"title":"Close Form Solution for Dielectric Cylindrical Shell in Fractional Dimensional Space","authors":"Saeed Ahmed, M. Akbar, Muhammad Imran Shahzad","doi":"10.53560/ppasa(59-2)757","DOIUrl":"https://doi.org/10.53560/ppasa(59-2)757","url":null,"abstract":"We have studied the Laplacian equation in non-integer space which had been previously used to describe complex phenomena in physics and electromagnetism. We have applied this idea to a dielectric cylindrical shell to find the electric potential and field of a dielectric coated cylinder analytically in fractional dimensional space. The problem is derived using Gegenbauer polynomials. This close form gneral solution solved in fractional dimensional space can be applied for various materials of cylindrical shell, outside shell and inside the cylindrical core. The obtained solution is retrieved for integer order by setting the fractional parameter α=3.","PeriodicalId":36961,"journal":{"name":"Proceedings of the Pakistan Academy of Sciences: Part A","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43272191","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The problem related to the dielectric cylinder placed in non-integer dimensional space (FD space) isthoroughly investigated in this paper. The FD space describes complex phenomena of physics and electromagnetism. We have solved Laplacian equation in FD space to obtain the solution of a dielectric cylinder in low frequency. The problem is solved by the method of separation of variables analytically. The classical solution of the problem can be easily recovered from the derived solution in non-integer dimensional space.
{"title":"Evaluation of Electric Field for a Dielectric Cylinder Placed in Fractional Space","authors":"M. Akbar, M. Shahzad, Saeed Ahmed","doi":"10.53560/ppasa(59-2)758","DOIUrl":"https://doi.org/10.53560/ppasa(59-2)758","url":null,"abstract":"The problem related to the dielectric cylinder placed in non-integer dimensional space (FD space) isthoroughly investigated in this paper. The FD space describes complex phenomena of physics and electromagnetism. We have solved Laplacian equation in FD space to obtain the solution of a dielectric cylinder in low frequency. The problem is solved by the method of separation of variables analytically. The classical solution of the problem can be easily recovered from the derived solution in non-integer dimensional space.","PeriodicalId":36961,"journal":{"name":"Proceedings of the Pakistan Academy of Sciences: Part A","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43919722","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Misbah Iram, Saif-Ur Rehman, S. Shahid, Sayeda Ambreen Mehmood
Sentiment Analysis (SA) is an efficient way of determining people’s opinions from a piece of text. SA using different social media sites such as Twitter has achieved tremendous results. Twitter is an online social media platform that contains a massive amount of data. The platform is known as an information channel corresponding to different sites and categories. Tweets are most often publicly accessible with very few limitations and security options available. Twitter also has powerful tools to enhance the utility of Twitter and a powerful search system to make publicly accessible the recently posted tweets by keyword. As popular social media, Twitter has the potential for interconnectivity of information, reviews, updates, and all of which are important to engage the targeted population. In this work, numerous methods that perform a classification of tweet sentiment on Twitter have been discussed. There has been an extensive research studies in the field of SA of Twitter data. This study provides a comprehensive analysis of the most standard and widely applicable opinion mining techniques based on machine learning and lexicon-based along with their metrics. The proposed work is helpful in informaiton analysis in the tweets where opinions are found heterogeneous, unstructured, polarised negative, positive, or neutral. In order to validate the supremacy of the suggested approach, we have executed a series of experiments on the real-world Twitter dataset that alters to show the effectiveness of the proposed framework. This research effort also highlighted the recent challenges in the SA field and the proposed work’s future scope.
{"title":"Anatomy of Sentiment Analysis of Tweets Using Machine Learning Approach","authors":"Misbah Iram, Saif-Ur Rehman, S. Shahid, Sayeda Ambreen Mehmood","doi":"10.53560/ppasa(59-2)771","DOIUrl":"https://doi.org/10.53560/ppasa(59-2)771","url":null,"abstract":"Sentiment Analysis (SA) is an efficient way of determining people’s opinions from a piece of text. SA using different social media sites such as Twitter has achieved tremendous results. Twitter is an online social media platform that contains a massive amount of data. The platform is known as an information channel corresponding to different sites and categories. Tweets are most often publicly accessible with very few limitations and security options available. Twitter also has powerful tools to enhance the utility of Twitter and a powerful search system to make publicly accessible the recently posted tweets by keyword. As popular social media, Twitter has the potential for interconnectivity of information, reviews, updates, and all of which are important to engage the targeted population. In this work, numerous methods that perform a classification of tweet sentiment on Twitter have been discussed. There has been an extensive research studies in the field of SA of Twitter data. This study provides a comprehensive analysis of the most standard and widely applicable opinion mining techniques based on machine learning and lexicon-based along with their metrics. The proposed work is helpful in informaiton analysis in the tweets where opinions are found heterogeneous, unstructured, polarised negative, positive, or neutral. In order to validate the supremacy of the suggested approach, we have executed a series of experiments on the real-world Twitter dataset that alters to show the effectiveness of the proposed framework. This research effort also highlighted the recent challenges in the SA field and the proposed work’s future scope. ","PeriodicalId":36961,"journal":{"name":"Proceedings of the Pakistan Academy of Sciences: Part A","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45104084","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Advanced Chinese Pressurized Water Reactor (ACP1000) is a third generation load following nuclear reactor. ACP1000 is designed to control the reactor power by a sophisticated control rod mechanism under the base load normal operation of a nuclear power plant in Mode-G. To extend the normal operation of ACP1000 for load following condition, boron adjustment control is used in manual configuration. In this research work, model based two new controllers are designed for ACP1000 reactor dynamics. A nonlinear two-point reactor kinetics model is developed for two halves of the reactor core designated as top and bottom of reactor core. Reactor feedbacks model for two-point reactor kinetics model is developed with fuel temperature, moderator temperature, Xenon concentration, G-Bank control rod position, R-Bank control rod position and boron concentration feedbacks under normal operation of ACP1000. Two problems of the large reactor core of ACP1000 are Xenon oscillations and axial offset in core power distribution. To address these problems, two new controllers are designed for normal load following operation of ACP1000. One controller is designed to replace G1-Bank and R-Bank in Mode-G for reactor power control. The second controller is designed to replace G2-Bank in Mode-G for reactivity control and axial power distribution control. Originally, both reactor coolant average temperature controller and reactor power controller were adaptive controllers. Therefore, both new controllers are designed based on an optimized sliding algorithm using a dedicated fractional order sliding mode control oriented adaptive fuzzy logic control (FO-SMC-AFLC) synthesis scheme. The performance of the proposed closed loop controllers is evaluated for design step and ramp power transients. Both proposed controllers are validated against benchmark results reported in Preliminary Safety Analysis Report (PSAR) of ACP1000. The novel control design scheme is proved satisfactory for normal load following operation of ACP1000, and all the results are found well within design limits.
{"title":"Design of Fractional Order Sliding Mode Adaptive Fuzzy Switching Controllers for Uncertain ACP1000 Nuclear Reactor Dynamics","authors":"Arshad H. Malik, Aftab A. Memon, Feroza Arshad","doi":"10.53560/ppasa(59-2)760","DOIUrl":"https://doi.org/10.53560/ppasa(59-2)760","url":null,"abstract":"Advanced Chinese Pressurized Water Reactor (ACP1000) is a third generation load following nuclear reactor. ACP1000 is designed to control the reactor power by a sophisticated control rod mechanism under the base load normal operation of a nuclear power plant in Mode-G. To extend the normal operation of ACP1000 for load following condition, boron adjustment control is used in manual configuration. In this research work, model based two new controllers are designed for ACP1000 reactor dynamics. A nonlinear two-point reactor kinetics model is developed for two halves of the reactor core designated as top and bottom of reactor core. Reactor feedbacks model for two-point reactor kinetics model is developed with fuel temperature, moderator temperature, Xenon concentration, G-Bank control rod position, R-Bank control rod position and boron concentration feedbacks under normal operation of ACP1000. Two problems of the large reactor core of ACP1000 are Xenon oscillations and axial offset in core power distribution. To address these problems, two new controllers are designed for normal load following operation of ACP1000. One controller is designed to replace G1-Bank and R-Bank in Mode-G for reactor power control. The second controller is designed to replace G2-Bank in Mode-G for reactivity control and axial power distribution control. Originally, both reactor coolant average temperature controller and reactor power controller were adaptive controllers. Therefore, both new controllers are designed based on an optimized sliding algorithm using a dedicated fractional order sliding mode control oriented adaptive fuzzy logic control (FO-SMC-AFLC) synthesis scheme. The performance of the proposed closed loop controllers is evaluated for design step and ramp power transients. Both proposed controllers are validated against benchmark results reported in Preliminary Safety Analysis Report (PSAR) of ACP1000. The novel control design scheme is proved satisfactory for normal load following operation of ACP1000, and all the results are found well within design limits.","PeriodicalId":36961,"journal":{"name":"Proceedings of the Pakistan Academy of Sciences: Part A","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42188201","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper using a q-difference operator, a class of meromorphic univalent functions with fixed second positive coefficients is defined. Coefficient estimates, some distortion theorems and other properties for this class are obtained. Various results obtained are sharp.
{"title":"Class of Meromorphic Univalent Functions with Fixed Second Positive Coefficients Defined by q-Difference Operator","authors":"Zienab M. Saleh, A. Mostafa","doi":"10.53560/ppasa(59-1)640","DOIUrl":"https://doi.org/10.53560/ppasa(59-1)640","url":null,"abstract":"In this paper using a q-difference operator, a class of meromorphic univalent functions with fixed second positive coefficients is defined. Coefficient estimates, some distortion theorems and other properties for this class are obtained. Various results obtained are sharp.","PeriodicalId":36961,"journal":{"name":"Proceedings of the Pakistan Academy of Sciences: Part A","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47610570","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This study aimed to explore the extent and evaluation of flash flood resilience in mountainous communities of Daral and Chail valleys of Swat. After collecting data from primary and secondary sources, the parameters of Disaster Resilience Capacity (DRC) model was applied for data analysis. The analysis reveals that stream discharge increases during summer mainly because of the rapid melting of snow, ice, glaciers and monsoonal rains, which results in flash floods. The communities living in the mountainous areas of Daral and Chail valleys face problems of multitudes of socio-economic and infrastructural flash flood damages almost every year. However, limited communities have adopted indigenous resilience strategies to bounce back from the recurrent adverse impacts of flash floods. It was found from the analysis that due to indigenous resilience practices by the local communities and the location of most mountainous communities, Daral valley is more resilient to flash floods as compared to Chail valley. Contrary to this, the extent and level of flash flood resilience in Chail valley are low as most of the mountainous communities are more vulnerable to seasonal flash floods. Some wise practices can enhance resilience to flash floods, especially land use planning, community preparedness, afforestation, and improved accessibility and communications.
{"title":"Extent and Evaluation of Flash Flood Resilience in Mountainous Communities of Daral and Chail Valleys, District Swat, Pakistan","authors":"Muhammad Khan, Atta-ur-Rahman","doi":"10.53560/ppasa(59-1)618","DOIUrl":"https://doi.org/10.53560/ppasa(59-1)618","url":null,"abstract":"This study aimed to explore the extent and evaluation of flash flood resilience in mountainous communities of Daral and Chail valleys of Swat. After collecting data from primary and secondary sources, the parameters of Disaster Resilience Capacity (DRC) model was applied for data analysis. The analysis reveals that stream discharge increases during summer mainly because of the rapid melting of snow, ice, glaciers and monsoonal rains, which results in flash floods. The communities living in the mountainous areas of Daral and Chail valleys face problems of multitudes of socio-economic and infrastructural flash flood damages almost every year. However, limited communities have adopted indigenous resilience strategies to bounce back from the recurrent adverse impacts of flash floods. It was found from the analysis that due to indigenous resilience practices by the local communities and the location of most mountainous communities, Daral valley is more resilient to flash floods as compared to Chail valley. Contrary to this, the extent and level of flash flood resilience in Chail valley are low as most of the mountainous communities are more vulnerable to seasonal flash floods. Some wise practices can enhance resilience to flash floods, especially land use planning, community preparedness, afforestation, and improved accessibility and communications.","PeriodicalId":36961,"journal":{"name":"Proceedings of the Pakistan Academy of Sciences: Part A","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43293693","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Atteeq Razzak, M. H. Zaheer, Muhammad Bilal Khan, Zaheer Uddin
Root finding Methods like the Bisection Method, Newton Raphson Method, Secant Method, and False Position Method have been revisited through a new approach. EACH METHOD’S user-friendly GUI computer programs have been developed on an Excel spreadsheet. A root locator graph is introduced in the spreadsheets, which helps identify the initial guess(es) required to calculate root using these methods. All real roots are now easily calculable by any of the four methods. The detailed steps to calculate roots are also shown on the spreadsheet. The spreadsheet can be made ready for the next calculation with a single click. We have developed a technique for Excel that helps accept polynomial in variable ‘x’ without directly mentioning cell location.
{"title":"Root Finding Methods Through GUI in Spreadsheets","authors":"Atteeq Razzak, M. H. Zaheer, Muhammad Bilal Khan, Zaheer Uddin","doi":"10.53560/ppasa(59-1)644","DOIUrl":"https://doi.org/10.53560/ppasa(59-1)644","url":null,"abstract":"Root finding Methods like the Bisection Method, Newton Raphson Method, Secant Method, and False Position Method have been revisited through a new approach. EACH METHOD’S user-friendly GUI computer programs have been developed on an Excel spreadsheet. A root locator graph is introduced in the spreadsheets, which helps identify the initial guess(es) required to calculate root using these methods. All real roots are now easily calculable by any of the four methods. The detailed steps to calculate roots are also shown on the spreadsheet. The spreadsheet can be made ready for the next calculation with a single click. We have developed a technique for Excel that helps accept polynomial in variable ‘x’ without directly mentioning cell location.","PeriodicalId":36961,"journal":{"name":"Proceedings of the Pakistan Academy of Sciences: Part A","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47796565","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：