Pub Date : 2020-11-01DOI: 10.22034/CMDE.2020.26116.1331
Neda Mohamadi, A. Soheili, F. Toutounian
In this paper, a denoising PDE model based on a combination of the isotropic diffusion and total variation models is presented. The new weighted model is able to be adaptive in each region in accordance with the image’s information. The model performs more diffusion in the flat regions of the image, and less diffusion in the edges of the image. The new model has more ability to restore the image in terms of peak signal to noise ratio and visual quality, compared with total variation, isotropic diffusion, and some well-known models. Experimental results show that the model is able to suppress the noise effectively while preserving texture features and edge information well.
{"title":"A Denoising PDE Model based on Isotropic Diffusion and Total Variation Models","authors":"Neda Mohamadi, A. Soheili, F. Toutounian","doi":"10.22034/CMDE.2020.26116.1331","DOIUrl":"https://doi.org/10.22034/CMDE.2020.26116.1331","url":null,"abstract":"In this paper, a denoising PDE model based on a combination of the isotropic diffusion and total variation models is presented. The new weighted model is able to be adaptive in each region in accordance with the image’s information. The model performs more diffusion in the flat regions of the image, and less diffusion in the edges of the image. The new model has more ability to restore the image in terms of peak signal to noise ratio and visual quality, compared with total variation, isotropic diffusion, and some well-known models. Experimental results show that the model is able to suppress the noise effectively while preserving texture features and edge information well.","PeriodicalId":44352,"journal":{"name":"Computational Methods for Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2020-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47085348","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 : 2020-11-01DOI: 10.22034/CMDE.2020.27847.1377
Homa Zadvan, J. Rashidinia
In this paper we develop a non polynomial cubic spline functions which we called ”TS spline”, based on trigonometric functions. The convergence analysis of this spline is investigated in details. The definition of B-spline basis function for TS spline is extended and ”TS B-spline” is introduced. This paper attempts to develop collocation method based on this B-spline for the numerical solution of the nonlinear Klein-Gordon equation. The convergence analysis of this approach is discussed, the second order of convergence is proved consequently. The proposed method is applied on some test examples and the numerical results are compared with those already available in literature. Observed errors in the solutions show the efficiency and numerical applicability of the proposed method.
{"title":"Development of non polynomial spline and New B-spline with application to solution of Klein-Gordon equation","authors":"Homa Zadvan, J. Rashidinia","doi":"10.22034/CMDE.2020.27847.1377","DOIUrl":"https://doi.org/10.22034/CMDE.2020.27847.1377","url":null,"abstract":"In this paper we develop a non polynomial cubic spline functions which we called ”TS spline”, based on trigonometric functions. The convergence analysis of this spline is investigated in details. The definition of B-spline basis function for TS spline is extended and ”TS B-spline” is introduced. This paper attempts to develop collocation method based on this B-spline for the numerical solution of the nonlinear Klein-Gordon equation. The convergence analysis of this approach is discussed, the second order of convergence is proved consequently. The proposed method is applied on some test examples and the numerical results are compared with those already available in literature. Observed errors in the solutions show the efficiency and numerical applicability of the proposed method.","PeriodicalId":44352,"journal":{"name":"Computational Methods for Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2020-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45013654","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 : 2020-11-01DOI: 10.22034/CMDE.2020.27817.1374
Hasan Barzegar Kelishami, M. A. Araghi, M. Amirfakhrian
One of the schemes to find the optimal shape parameter and optimal number of points in the radial basis function (RBF) methods is to apply the stochastic arithmetic (SA) in place of the common floating-point arithmetic (FPA). The main purpose of this work is to introduce a reliable approach based on this new arithmetic to compute the local optimal shape parameter and number of points in multiquadric and Gaussian RBF-meshless methods for solving differential equations, in the iterative process. To this end, the CESTAC method is applied. Also, in order to implement the proposed algorithms, the CADNA library is performed. The examples illustrate the efficiency and importance of using this library to validate the results.
{"title":"The use of CESTAC method to find optimal shape parameter and optimal number of points in RBF-meshless methods to solve differential equations","authors":"Hasan Barzegar Kelishami, M. A. Araghi, M. Amirfakhrian","doi":"10.22034/CMDE.2020.27817.1374","DOIUrl":"https://doi.org/10.22034/CMDE.2020.27817.1374","url":null,"abstract":"One of the schemes to find the optimal shape parameter and optimal number of points in the radial basis function (RBF) methods is to apply the stochastic arithmetic (SA) in place of the common floating-point arithmetic (FPA). The main purpose of this work is to introduce a reliable approach based on this new arithmetic to compute the local optimal shape parameter and number of points in multiquadric and Gaussian RBF-meshless methods for solving differential equations, in the iterative process. To this end, the CESTAC method is applied. Also, in order to implement the proposed algorithms, the CADNA library is performed. The examples illustrate the efficiency and importance of using this library to validate the results.","PeriodicalId":44352,"journal":{"name":"Computational Methods for Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2020-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42638265","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 : 2020-11-01DOI: 10.22034/CMDE.2020.32830.1527
M. Adiyaman, B. Noyan
In this paper, the nonlinear system of initial value problems are solved numerically by using Residual method which is based on the minimizing residual function by the Taylor’s series expansion. The convergence analysis of the method is given. The significant feature of the method is reduction of nonlinear system of initial value problems to the system of linear equations. To emphasize the accuracy and potential of the method, we solve Lorenz system and primary HIV-1 infection problem numerically
{"title":"Residual Method for Nonlinear System of Initial Value Problems","authors":"M. Adiyaman, B. Noyan","doi":"10.22034/CMDE.2020.32830.1527","DOIUrl":"https://doi.org/10.22034/CMDE.2020.32830.1527","url":null,"abstract":"In this paper, the nonlinear system of initial value problems are solved numerically by using Residual method which is based on the minimizing residual function by the Taylor’s series expansion. The convergence analysis of the method is given. The significant feature of the method is reduction of nonlinear system of initial value problems to the system of linear equations. To emphasize the accuracy and potential of the method, we solve Lorenz system and primary HIV-1 infection problem numerically","PeriodicalId":44352,"journal":{"name":"Computational Methods for Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2020-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47413171","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 : 2020-11-01DOI: 10.22034/CMDE.2020.31627.1479
A. Mohammadi, N. Aghazadeh, S. Rezapour
The present study applies the Picard iterative method to nonlinear singular partial fractional differential equations. The Haar and second-kind Chebyshev wavelets operational matrix of fractional integration will be used to solve problems combining linearization technique with the Picard method. The singular problem will be converted to an algebraic system of equations, which can be easily solved. Numerical examples are provided to illustrate the efficiency and accuracy of the technique.
{"title":"Wavelet-Picard iterative method for solving singular fractional nonlinear partial differential equations with initial and boundary conditions","authors":"A. Mohammadi, N. Aghazadeh, S. Rezapour","doi":"10.22034/CMDE.2020.31627.1479","DOIUrl":"https://doi.org/10.22034/CMDE.2020.31627.1479","url":null,"abstract":"The present study applies the Picard iterative method to nonlinear singular partial fractional differential equations. The Haar and second-kind Chebyshev wavelets operational matrix of fractional integration will be used to solve problems combining linearization technique with the Picard method. The singular problem will be converted to an algebraic system of equations, which can be easily solved. Numerical examples are provided to illustrate the efficiency and accuracy of the technique.","PeriodicalId":44352,"journal":{"name":"Computational Methods for Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2020-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46265033","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 : 2020-09-22DOI: 10.22034/CMDE.2020.40380.1764
A. Neisy
Nowadays, the fixed interest rate financing method is commonly used in the capitalist financial system and in a wide range of financial liability instruments, the most important of which is bond. In the Islamic financial system, using these instruments is considered as usury and has been prohibited. In fact, Islamic law, Shari’ah, forbids Muslims from receiving or paying off the Riba. Therefore, using customary financial instruments such as bond is not acceptable or applicable in countries which have a majority of Muslim citizens. In this paper, we introduce one financial instrument, Sukuk, as a securities-based asset under stochastic income. These securities can be traded in secondary markets based on the Shari’ah law. To this end, this paper will focus on the most common structure of the Islamic bond, the Ijarah sukuk and its negotiation mechanism. Then, by presenting the short-term stochastic model, we solve fixed interest rate and model the securities-based asset by the stochastic model. Finally, we approximate the resulting model by radial basis function method, as well as utilizing the Matlab software
{"title":"Meshless approach for pricing Islamic Ijarah under stochastic interest rate models","authors":"A. Neisy","doi":"10.22034/CMDE.2020.40380.1764","DOIUrl":"https://doi.org/10.22034/CMDE.2020.40380.1764","url":null,"abstract":"Nowadays, the fixed interest rate financing method is commonly used in the capitalist financial system and in a wide range of financial liability instruments, the most important of which is bond. In the Islamic financial system, using these instruments is considered as usury and has been prohibited. In fact, Islamic law, Shari’ah, forbids Muslims from receiving or paying off the Riba. Therefore, using customary financial instruments such as bond is not acceptable or applicable in countries which have a majority of Muslim citizens. In this paper, we introduce one financial instrument, Sukuk, as a securities-based asset under stochastic income. These securities can be traded in secondary markets based on the Shari’ah law. To this end, this paper will focus on the most common structure of the Islamic bond, the Ijarah sukuk and its negotiation mechanism. Then, by presenting the short-term stochastic model, we solve fixed interest rate and model the securities-based asset by the stochastic model. Finally, we approximate the resulting model by radial basis function method, as well as utilizing the Matlab software","PeriodicalId":44352,"journal":{"name":"Computational Methods for Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2020-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46081695","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 : 2020-08-01DOI: 10.22034/CMDE.2020.29576.1424
Seyyedeh Roodabeh Moosavi, N. Taghizadeh, J. Manafian
In this work, an initial-boundary value problem with a non-classic condition for the one-dimensional wave equation is presented and the reduced differential transform method is applied to ascertain the solution of the problem. We will investigate a new kind of non-local boundary value problems in which are the solution of hyperbolic partial differential equations with a non-standard boundary specification. The advantage of this method is its simplicity in using, it solves the problem directly and straightforward without using perturbation, linearization, Adomian’s polynomial or any other transformation and gives the solution in the form of convergent power series with simply determinable components. Also, the convergence of the method is proved and seven examples are tested to shows the competency of our study.
{"title":"Analytical approximations of one-dimensional hyperbolic equation with non-local integral conditions by reduced differential transform method","authors":"Seyyedeh Roodabeh Moosavi, N. Taghizadeh, J. Manafian","doi":"10.22034/CMDE.2020.29576.1424","DOIUrl":"https://doi.org/10.22034/CMDE.2020.29576.1424","url":null,"abstract":"In this work, an initial-boundary value problem with a non-classic condition for the one-dimensional wave equation is presented and the reduced differential transform method is applied to ascertain the solution of the problem. We will investigate a new kind of non-local boundary value problems in which are the solution of hyperbolic partial differential equations with a non-standard boundary specification. The advantage of this method is its simplicity in using, it solves the problem directly and straightforward without using perturbation, linearization, Adomian’s polynomial or any other transformation and gives the solution in the form of convergent power series with simply determinable components. Also, the convergence of the method is proved and seven examples are tested to shows the competency of our study.","PeriodicalId":44352,"journal":{"name":"Computational Methods for Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2020-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48957167","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 : 2020-08-01DOI: 10.22034/CMDE.2020.31374.1471
H. Baskonus, E. Eskitaşçioğlu
In this paper, we apply an analytical method, namely, the sine-Gordon expansion method and extract some complex optical soliton solutions to the (2+1)-dimensional extended shallow water wave model, which describes the evolution of shallow water wave propagation. We obtain some complex mixed-dark and bright soliton solutions to this nonlinear model. Considering some suitable values of parameters, we plot the various dimensional simulations of every results found in this manuscript. We observe that our result may be useful in detecting some complex waves behaviors.
{"title":"Complex Wave Surfaces to the Extended Shallow Water Wave Model with (2+1)-dimensional","authors":"H. Baskonus, E. Eskitaşçioğlu","doi":"10.22034/CMDE.2020.31374.1471","DOIUrl":"https://doi.org/10.22034/CMDE.2020.31374.1471","url":null,"abstract":"In this paper, we apply an analytical method, namely, the sine-Gordon expansion method and extract some complex optical soliton solutions to the (2+1)-dimensional extended shallow water wave model, which describes the evolution of shallow water wave propagation. We obtain some complex mixed-dark and bright soliton solutions to this nonlinear model. Considering some suitable values of parameters, we plot the various dimensional simulations of every results found in this manuscript. We observe that our result may be useful in detecting some complex waves behaviors.","PeriodicalId":44352,"journal":{"name":"Computational Methods for Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2020-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43303590","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 : 2020-08-01DOI: 10.22034/CMDE.2020.31527.1475
Ghader Ahmadnezhad, N. Aghazadeh, S. Rezapour
In this work, we investigate fractional version of the Fisher equation and solve it by using an efficient iteration technique based on the Haar wavelet operational matrices. In fact, we convert the nonlinear equation into a Sylvester equation by the Haar wavelet collocation iteration method (HWCIM) to obtain the solution. We provide four numerical examples to illustrate the simplicity and efficiency of the technique.
{"title":"Haar wavelet iteration method for solving time fractional Fisher's equation","authors":"Ghader Ahmadnezhad, N. Aghazadeh, S. Rezapour","doi":"10.22034/CMDE.2020.31527.1475","DOIUrl":"https://doi.org/10.22034/CMDE.2020.31527.1475","url":null,"abstract":"In this work, we investigate fractional version of the Fisher equation and solve it by using an efficient iteration technique based on the Haar wavelet operational matrices. In fact, we convert the nonlinear equation into a Sylvester equation by the Haar wavelet collocation iteration method (HWCIM) to obtain the solution. We provide four numerical examples to illustrate the simplicity and efficiency of the technique.","PeriodicalId":44352,"journal":{"name":"Computational Methods for Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2020-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43007230","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 : 2020-08-01DOI: 10.22034/CMDE.2020.29307.1414
A. Shokri, S. Mirzaei
In this paper, a pseudo-spectral method with the Lagrange polynomial basis is proposed to solve the time-fractional advection-diffusion equation. A semi-discrete approximation scheme is used for conversion of this equation to a system of ordinary fractional differential equations. Also, to protect the high accuracy of the spectral approximation, the Mittag-Leffler function is used for the integration along the time variable. Some examples are performed to illustrate the accuracy and efficiency of the proposed method.
{"title":"A pseudo-spectral based method for time-fractional advection-diffusion equation","authors":"A. Shokri, S. Mirzaei","doi":"10.22034/CMDE.2020.29307.1414","DOIUrl":"https://doi.org/10.22034/CMDE.2020.29307.1414","url":null,"abstract":"In this paper, a pseudo-spectral method with the Lagrange polynomial basis is proposed to solve the time-fractional advection-diffusion equation. A semi-discrete approximation scheme is used for conversion of this equation to a system of ordinary fractional differential equations. Also, to protect the high accuracy of the spectral approximation, the Mittag-Leffler function is used for the integration along the time variable. Some examples are performed to illustrate the accuracy and efficiency of the proposed method.","PeriodicalId":44352,"journal":{"name":"Computational Methods for Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2020-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44893510","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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