Pub Date : 2023-07-05DOI: 10.3390/computation11070132
Aleksandr Alekseev, Z. Mingaleva, I. Alekseeva, E. Lobova, Alexander Oksman, Alexander Mitrofanov
Risk involves identifying several options that the decision-maker can opt for while making a choice either in the direction of risk or reliability. In this approach, risk is defined as the action of the subject which will lead to the loss or guaranteed safety of what has been achieved. As the uncertainty of the external business environment increases for companies, the task of managing risks both individually and as a set of risks becomes more and more relevant. The purpose of this study is to solve the problem of managing multifactorial risks using mathematical methods for determining the optimal risk management trajectories separately for each factor. To determine the optimal risk management trajectories for each factor, a numerical method is used based on the choice of the most effective direction, which is defined as the ratio of risk change to cost change. An information system prototype has been created that can support the management of a set of risks. Approbation of the information system was carried out on an example containing two conceptual risk factors. The proposed prototype builds a three-dimensional risk map by interpolating the risk matrix entered by the risk manager using an additive–multiplicative aggregation procedure, as well as optimal risk management trajectories for all entered risk factors.
{"title":"Developing a Numerical Method of Risk Management Taking into Account the Decision-Maker's Subjective Attitude Towards Multifactorial Risks","authors":"Aleksandr Alekseev, Z. Mingaleva, I. Alekseeva, E. Lobova, Alexander Oksman, Alexander Mitrofanov","doi":"10.3390/computation11070132","DOIUrl":"https://doi.org/10.3390/computation11070132","url":null,"abstract":"Risk involves identifying several options that the decision-maker can opt for while making a choice either in the direction of risk or reliability. In this approach, risk is defined as the action of the subject which will lead to the loss or guaranteed safety of what has been achieved. As the uncertainty of the external business environment increases for companies, the task of managing risks both individually and as a set of risks becomes more and more relevant. The purpose of this study is to solve the problem of managing multifactorial risks using mathematical methods for determining the optimal risk management trajectories separately for each factor. To determine the optimal risk management trajectories for each factor, a numerical method is used based on the choice of the most effective direction, which is defined as the ratio of risk change to cost change. An information system prototype has been created that can support the management of a set of risks. Approbation of the information system was carried out on an example containing two conceptual risk factors. The proposed prototype builds a three-dimensional risk map by interpolating the risk matrix entered by the risk manager using an additive–multiplicative aggregation procedure, as well as optimal risk management trajectories for all entered risk factors.","PeriodicalId":10526,"journal":{"name":"Comput.","volume":"7 1","pages":"132"},"PeriodicalIF":0.0,"publicationDate":"2023-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83520700","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}
Pub Date : 2023-07-05DOI: 10.3390/computation11070131
H. Jalghaf, Endre Kovács, I. F. Barna, László Mátyás
New analytical solutions of the heat conduction equation obtained by utilizing a self-similar Ansatz are presented in cylindrical and spherical coordinates. Then, these solutions are reproduced with high accuracy using recent explicit and unconditionally stable finite difference methods. After this, real experimental data from the literature regarding a heated cylinder are reproduced using the explicit numerical methods as well as using Finite Element Methods (FEM) ANSYS workbench. Convection and nonlinear radiation are also considered on the boundary of the cylinder. The verification results showed that the numerical methods have a high accuracy to deal with cylindrical and spherical bodies; also, the comparison of the temperatures for all approaches showed that the explicit methods are more accurate than the commercial software.
{"title":"Analytical Solution and Numerical Simulation of Heat Transfer in Cylindrical- and Spherical-Shaped Bodies","authors":"H. Jalghaf, Endre Kovács, I. F. Barna, László Mátyás","doi":"10.3390/computation11070131","DOIUrl":"https://doi.org/10.3390/computation11070131","url":null,"abstract":"New analytical solutions of the heat conduction equation obtained by utilizing a self-similar Ansatz are presented in cylindrical and spherical coordinates. Then, these solutions are reproduced with high accuracy using recent explicit and unconditionally stable finite difference methods. After this, real experimental data from the literature regarding a heated cylinder are reproduced using the explicit numerical methods as well as using Finite Element Methods (FEM) ANSYS workbench. Convection and nonlinear radiation are also considered on the boundary of the cylinder. The verification results showed that the numerical methods have a high accuracy to deal with cylindrical and spherical bodies; also, the comparison of the temperatures for all approaches showed that the explicit methods are more accurate than the commercial software.","PeriodicalId":10526,"journal":{"name":"Comput.","volume":"1 1","pages":"131"},"PeriodicalIF":0.0,"publicationDate":"2023-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79022282","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}
Pub Date : 2023-07-04DOI: 10.3390/computers12070135
A. Celesti, I. D. Falco, A. Galletta, Giovanna Sannino
Machine and deep learning techniques are fuelling a revolution in the health domain and are attracting the interest of many cross-disciplinary research groups all over the world [...]
机器和深度学习技术正在推动健康领域的革命，并吸引了世界各地许多跨学科研究小组的兴趣[…]
{"title":"Special Issue \"Advances in Machine and Deep Learning in the Health Domain\"","authors":"A. Celesti, I. D. Falco, A. Galletta, Giovanna Sannino","doi":"10.3390/computers12070135","DOIUrl":"https://doi.org/10.3390/computers12070135","url":null,"abstract":"Machine and deep learning techniques are fuelling a revolution in the health domain and are attracting the interest of many cross-disciplinary research groups all over the world [...]","PeriodicalId":10526,"journal":{"name":"Comput.","volume":"11 1","pages":"135"},"PeriodicalIF":0.0,"publicationDate":"2023-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87480236","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}
Pub Date : 2023-07-03DOI: 10.3390/computation11070130
M. Izadi, H. M. Srivastava
We propose two accurate and efficient spectral collocation techniques based on a (novel) domain-splitting strategy to handle a nonlinear fractional system consisting of three ODEs arising in financial modeling and with chaotic behavior. One of the major numerical difficulties in designing traditional spectral methods is in the handling of model problems on a long computational domain, which usually yields to loss of accuracy. One remedy is to split the underlying domain and apply the spectral method locally in each subdomain rather than on the global domain of interest. To treat the chaotic financial system numerically, we use the generalized version of modified Bessel polynomials (GMBPs) in the collocation matrix approaches along with the domain-splitting strategy. Whereas the first matrix collocation scheme is directly applied to the financial model problem, the second one is a combination of the quasilinearization method and the direct first numerical matrix method. In the former approach, we arrive at nonlinear algebraic matrix equations while the resulting systems are linear in the latter method and can be solved more efficiently. A convergence theorem related to GMBPs is proved and an upper bound for the error is derived. Several simulation outcomes are provided to show the utility and applicability of the presented matrix collocation procedures.
{"title":"Applications of Modified Bessel Polynomials to Solve a Nonlinear Chaotic Fractional-Order System in the Financial Market: Domain-Splitting Collocation Techniques","authors":"M. Izadi, H. M. Srivastava","doi":"10.3390/computation11070130","DOIUrl":"https://doi.org/10.3390/computation11070130","url":null,"abstract":"We propose two accurate and efficient spectral collocation techniques based on a (novel) domain-splitting strategy to handle a nonlinear fractional system consisting of three ODEs arising in financial modeling and with chaotic behavior. One of the major numerical difficulties in designing traditional spectral methods is in the handling of model problems on a long computational domain, which usually yields to loss of accuracy. One remedy is to split the underlying domain and apply the spectral method locally in each subdomain rather than on the global domain of interest. To treat the chaotic financial system numerically, we use the generalized version of modified Bessel polynomials (GMBPs) in the collocation matrix approaches along with the domain-splitting strategy. Whereas the first matrix collocation scheme is directly applied to the financial model problem, the second one is a combination of the quasilinearization method and the direct first numerical matrix method. In the former approach, we arrive at nonlinear algebraic matrix equations while the resulting systems are linear in the latter method and can be solved more efficiently. A convergence theorem related to GMBPs is proved and an upper bound for the error is derived. Several simulation outcomes are provided to show the utility and applicability of the presented matrix collocation procedures.","PeriodicalId":10526,"journal":{"name":"Comput.","volume":"67 1","pages":"130"},"PeriodicalIF":0.0,"publicationDate":"2023-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84051483","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}
Pub Date : 2023-07-02DOI: 10.3390/computation11070129
N. Vitanov, Z. Dimitrova
We studied obtaining exact solutions to a set of equations related to the SEIR (Susceptible-Exposed-Infectious-Recovered) model of epidemic spread. These solutions may be used to model epidemic waves. We transformed the SEIR model into a differential equation that contained an exponential nonlinearity. This equation was then approximated by a set of differential equations which contained polynomial nonlinearities. We solved several equations from the set using the Simple Equations Method (SEsM). In doing so, we obtained many new exact solutions to the corresponding equations. Several of these solutions can describe the evolution of epidemic waves that affect a small percentage of individuals in the population. Such waves have frequently been observed in the COVID-19 pandemic in recent years. The discussion shows that SEsM is an effective methodology for computing exact solutions to nonlinear differential equations. The exact solutions obtained can help us to understand the evolution of various processes in the modeled systems. In the specific case of the SEIR model, some of the exact solutions can help us to better understand the evolution of the quantities connected to the epidemic waves.
{"title":"Computation of the Exact Forms of Waves for a Set of Differential Equations Associated with the SEIR Model of Epidemics","authors":"N. Vitanov, Z. Dimitrova","doi":"10.3390/computation11070129","DOIUrl":"https://doi.org/10.3390/computation11070129","url":null,"abstract":"We studied obtaining exact solutions to a set of equations related to the SEIR (Susceptible-Exposed-Infectious-Recovered) model of epidemic spread. These solutions may be used to model epidemic waves. We transformed the SEIR model into a differential equation that contained an exponential nonlinearity. This equation was then approximated by a set of differential equations which contained polynomial nonlinearities. We solved several equations from the set using the Simple Equations Method (SEsM). In doing so, we obtained many new exact solutions to the corresponding equations. Several of these solutions can describe the evolution of epidemic waves that affect a small percentage of individuals in the population. Such waves have frequently been observed in the COVID-19 pandemic in recent years. The discussion shows that SEsM is an effective methodology for computing exact solutions to nonlinear differential equations. The exact solutions obtained can help us to understand the evolution of various processes in the modeled systems. In the specific case of the SEIR model, some of the exact solutions can help us to better understand the evolution of the quantities connected to the epidemic waves.","PeriodicalId":10526,"journal":{"name":"Comput.","volume":"64 1","pages":"129"},"PeriodicalIF":0.0,"publicationDate":"2023-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76616654","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}
Pub Date : 2023-07-01DOI: 10.3390/computers12070134
Are Dæhlen, I. Heldal, Qasim Ali
Oculomotor dysfunctions (OMDs) are problems relating to coordination and accuracy of eye movements for processing visual information. Eye-tracking (ET) technologies show great promise in the identification of OMDs. However, current computer technologies for vision screening are specialized devices with limited screen size and the inability to measure depth, while visual field and depth are important information for detecting OMDs. In this experimental study, we examine the possibilities of immersive virtual reality (VR) technologies compared with laptop technologies for increased user experiences, presence, immersiveness, and the use of serious games for identifying OMDs. The results present increased interest in VR-based screening, motivating users to focus better using VR applications free from outside distractions. These limitations currently include lower performance and confidence in results of identifying OMDs with the used HMDs. Using serious games for screening in VR is also estimated to have great potential for developing a more robust vision screening tool, especially for younger children.
{"title":"Technologies Supporting Screening Oculomotor Problems: Challenges for Virtual Reality","authors":"Are Dæhlen, I. Heldal, Qasim Ali","doi":"10.3390/computers12070134","DOIUrl":"https://doi.org/10.3390/computers12070134","url":null,"abstract":"Oculomotor dysfunctions (OMDs) are problems relating to coordination and accuracy of eye movements for processing visual information. Eye-tracking (ET) technologies show great promise in the identification of OMDs. However, current computer technologies for vision screening are specialized devices with limited screen size and the inability to measure depth, while visual field and depth are important information for detecting OMDs. In this experimental study, we examine the possibilities of immersive virtual reality (VR) technologies compared with laptop technologies for increased user experiences, presence, immersiveness, and the use of serious games for identifying OMDs. The results present increased interest in VR-based screening, motivating users to focus better using VR applications free from outside distractions. These limitations currently include lower performance and confidence in results of identifying OMDs with the used HMDs. Using serious games for screening in VR is also estimated to have great potential for developing a more robust vision screening tool, especially for younger children.","PeriodicalId":10526,"journal":{"name":"Comput.","volume":"39 1","pages":"134"},"PeriodicalIF":0.0,"publicationDate":"2023-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81806844","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}
Pub Date : 2023-06-29DOI: 10.3390/computation11070126
Manolis Georgioudakis, V. Plevris
The dynamic analysis of structures is a computationally intensive procedure that must be considered, in order to make accurate seismic performance assessments in civil and structural engineering applications. To avoid these computationally demanding tasks, simplified methods are often used by engineers in practice, to estimate the behavior of complex structures under dynamic loading. This paper presents an assessment of several machine learning (ML) algorithms, with different characteristics, that aim to predict the dynamic analysis response of multi-story buildings. Large datasets of dynamic response analyses results were generated through standard sampling methods and conventional response spectrum modal analysis procedures. In an effort to obtain the best algorithm performance, an extensive hyper-parameter search was elaborated, followed by the corresponding feature importance. The ML model which exhibited the best performance was deployed in a web application, with the aim of providing predictions of the dynamic responses of multi-story buildings, according to their characteristics.
{"title":"Response Spectrum Analysis of Multi-Story Shear Buildings Using Machine Learning Techniques","authors":"Manolis Georgioudakis, V. Plevris","doi":"10.3390/computation11070126","DOIUrl":"https://doi.org/10.3390/computation11070126","url":null,"abstract":"The dynamic analysis of structures is a computationally intensive procedure that must be considered, in order to make accurate seismic performance assessments in civil and structural engineering applications. To avoid these computationally demanding tasks, simplified methods are often used by engineers in practice, to estimate the behavior of complex structures under dynamic loading. This paper presents an assessment of several machine learning (ML) algorithms, with different characteristics, that aim to predict the dynamic analysis response of multi-story buildings. Large datasets of dynamic response analyses results were generated through standard sampling methods and conventional response spectrum modal analysis procedures. In an effort to obtain the best algorithm performance, an extensive hyper-parameter search was elaborated, followed by the corresponding feature importance. The ML model which exhibited the best performance was deployed in a web application, with the aim of providing predictions of the dynamic responses of multi-story buildings, according to their characteristics.","PeriodicalId":10526,"journal":{"name":"Comput.","volume":"56 1","pages":"126"},"PeriodicalIF":0.0,"publicationDate":"2023-06-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84601272","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}
Pub Date : 2023-06-29DOI: 10.3390/computation11070128
V. S. Reddy, Jagan Kandasamy, S. Sivanandam
This investigation focuses on the impact of Stefan blowing on the flow of hybrid nanoliquids over a moving slender needle with magnetohydrodynamics (MHD), thermal radiation, and entropy generation. To facilitate analysis, suitable transformations are applied to convert the governing partial differential equations into a set of ordinary differential equations, which are then solved analytically using Homotopy Analysis Method (HAM) in Mathematica. This study investigates how varying the values of Stefan blowing, magnetic field, and thermal radiation parameters impact the profiles of velocity, temperature, and concentration. Additionally, the study analyzes the outcomes of the local skin friction, local Nusselt number, and local Sherwood number. Increasing the magnetic field reduces the velocity profile. The temperature profile is enhanced by a rise in the thermal radiation parameter. Also, the results reveal that an increase in the Stefan blowing number leads to higher profiles of velocity.
{"title":"Stefan Blowing Impacts on Hybrid Nanofluid Flow over a Moving Thin Needle with Thermal Radiation and MHD","authors":"V. S. Reddy, Jagan Kandasamy, S. Sivanandam","doi":"10.3390/computation11070128","DOIUrl":"https://doi.org/10.3390/computation11070128","url":null,"abstract":"This investigation focuses on the impact of Stefan blowing on the flow of hybrid nanoliquids over a moving slender needle with magnetohydrodynamics (MHD), thermal radiation, and entropy generation. To facilitate analysis, suitable transformations are applied to convert the governing partial differential equations into a set of ordinary differential equations, which are then solved analytically using Homotopy Analysis Method (HAM) in Mathematica. This study investigates how varying the values of Stefan blowing, magnetic field, and thermal radiation parameters impact the profiles of velocity, temperature, and concentration. Additionally, the study analyzes the outcomes of the local skin friction, local Nusselt number, and local Sherwood number. Increasing the magnetic field reduces the velocity profile. The temperature profile is enhanced by a rise in the thermal radiation parameter. Also, the results reveal that an increase in the Stefan blowing number leads to higher profiles of velocity.","PeriodicalId":10526,"journal":{"name":"Comput.","volume":"18 1","pages":"128"},"PeriodicalIF":0.0,"publicationDate":"2023-06-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87127994","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}
Pub Date : 2023-06-29DOI: 10.20944/preprints202305.0919.v1
Angeliki Antoniou
When the majority of museums and other cultural institutions were shut down due to the pandemic, mixed museum visits became a hot issue. After the pandemic, mixed visits, in the opinion of many experts, would become the new norm for experiencing cultural content. Diverse types of mergers between online and onsite visits have already begun to be investigated by researchers, with the purpose of not only avoiding the spread of disease but also of enabling visits of people who were previously excluded, such as persons in remote geographic areas or people with mobility challenges. In fact, over the last three years, there have been rapid developments in mixed visits in cultural heritage sites. The current work takes into account a contextual model of museum learning to define potential use scenarios for visits from people of different cultural backgrounds and offers an evaluation of current practices. The new model that emerges, the contextual model of mixed visits, allows for the further study of the field, as it attempts to describe recent research efforts in four main contexts: mixed visits in the personal context, mixed visits in the socio-cultural context, mixed visits in the physical context, and temporality of mixed visits. Inductive analysis of a literature review allowed the extraction of relevant themes, examples from museums, as well as extraction of guidelines.
{"title":"Mixed Cultural Visits or What COVID-19 Taught Us","authors":"Angeliki Antoniou","doi":"10.20944/preprints202305.0919.v1","DOIUrl":"https://doi.org/10.20944/preprints202305.0919.v1","url":null,"abstract":"When the majority of museums and other cultural institutions were shut down due to the pandemic, mixed museum visits became a hot issue. After the pandemic, mixed visits, in the opinion of many experts, would become the new norm for experiencing cultural content. Diverse types of mergers between online and onsite visits have already begun to be investigated by researchers, with the purpose of not only avoiding the spread of disease but also of enabling visits of people who were previously excluded, such as persons in remote geographic areas or people with mobility challenges. In fact, over the last three years, there have been rapid developments in mixed visits in cultural heritage sites. The current work takes into account a contextual model of museum learning to define potential use scenarios for visits from people of different cultural backgrounds and offers an evaluation of current practices. The new model that emerges, the contextual model of mixed visits, allows for the further study of the field, as it attempts to describe recent research efforts in four main contexts: mixed visits in the personal context, mixed visits in the socio-cultural context, mixed visits in the physical context, and temporality of mixed visits. Inductive analysis of a literature review allowed the extraction of relevant themes, examples from museums, as well as extraction of guidelines.","PeriodicalId":10526,"journal":{"name":"Comput.","volume":"61 1","pages":"133"},"PeriodicalIF":0.0,"publicationDate":"2023-06-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73821331","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}
Pub Date : 2023-06-29DOI: 10.3390/computation11070127
A. Askar, A. Nagy, I. F. Barna, Endre Kovács
We utilize the travelling-wave Ansatz to obtain novel analytical solutions to the linear diffusion–reaction equation. The reaction term is a function of time and space simultaneously, firstly in a Lorentzian form and secondly in a cosine travelling-wave form. The new solutions contain the Heun functions in the first case and the Mathieu functions for the second case, and therefore are highly nontrivial. We use these solutions to test some non-conventional explicit and stable numerical methods against the standard explicit and implicit methods, where in the latter case the algebraic equation system is solved by the preconditioned conjugate gradient and the GMRES solvers. After this verification, we also calculate the transient temperature of a 2D surface subjected to the cooling effect of the wind, which is a function of space and time again. We obtain that the explicit stable methods can reach the accuracy of the implicit solvers in orders of magnitude shorter time.
{"title":"Analytical and Numerical Results for the Diffusion-Reaction Equation When the Reaction Coefficient Depends on Simultaneously the Space and Time Coordinates","authors":"A. Askar, A. Nagy, I. F. Barna, Endre Kovács","doi":"10.3390/computation11070127","DOIUrl":"https://doi.org/10.3390/computation11070127","url":null,"abstract":"We utilize the travelling-wave Ansatz to obtain novel analytical solutions to the linear diffusion–reaction equation. The reaction term is a function of time and space simultaneously, firstly in a Lorentzian form and secondly in a cosine travelling-wave form. The new solutions contain the Heun functions in the first case and the Mathieu functions for the second case, and therefore are highly nontrivial. We use these solutions to test some non-conventional explicit and stable numerical methods against the standard explicit and implicit methods, where in the latter case the algebraic equation system is solved by the preconditioned conjugate gradient and the GMRES solvers. After this verification, we also calculate the transient temperature of a 2D surface subjected to the cooling effect of the wind, which is a function of space and time again. We obtain that the explicit stable methods can reach the accuracy of the implicit solvers in orders of magnitude shorter time.","PeriodicalId":10526,"journal":{"name":"Comput.","volume":"4 1","pages":"127"},"PeriodicalIF":0.0,"publicationDate":"2023-06-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83507020","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}
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