Pub Date : 2021-06-29DOI: 10.22034/CMDE.2021.32807.1580
Wadhah Ahmed Alsadi, Wadhah Mokhtar Hussein, T. Q. S. Abdullah
In this literature, we study the existence and stability of the solution of the boundary value problem of fractional differential equations with $ Phi_{p} $-Laplacian operator. Our problem is based on Caputo fractional derivative of orders $ sigma,epsilon$, where $ k- 1
{"title":"Existence and stability criterion for the results of fractional order $ Phi_{p} $-Laplacian operator boundary value problem","authors":"Wadhah Ahmed Alsadi, Wadhah Mokhtar Hussein, T. Q. S. Abdullah","doi":"10.22034/CMDE.2021.32807.1580","DOIUrl":"https://doi.org/10.22034/CMDE.2021.32807.1580","url":null,"abstract":"In this literature, we study the existence and stability of the solution of the boundary value problem of fractional differential equations with $ Phi_{p} $-Laplacian operator. Our problem is based on Caputo fractional derivative of orders $ sigma,epsilon$, where $ k- 1<sigma,epsilonleq k $, and $ kgeq3 $. By using the Schauder fixed point theory and properties of the Green function, some conditions are established which show the criterion of the existence and non-existence solution for the proposed problem. We also investigate some adequate conditions for the Hyers-Ulam stability of the solution. Illustrated examples are given as an application of our result.","PeriodicalId":44352,"journal":{"name":"Computational Methods for Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2021-06-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42527130","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 : 2021-06-20DOI: 10.22034/CMDE.2021.43961.1864
P. Nabati
The rapid spread of coronavirus disease (COVID-19) has increased the attention to the mathematical modeling of spreading the disease in the world. The behavior of spreading is not deterministic in the last year. The purpose of this paper is to presents a stochastic differential equation for modeling the data sets of the COVID-19 involving infected, recovered, and death cases. At first, the time series of the covid-19 is modeling with the Ornstein-Uhlenbeck process and then using the Ito lemma and Euler approximation the analytical and numerical simulations for the stochastic differential equation are achieved. Parameters estimation is done using the maximum likelihood estimator. Finally, numerical simulations are performed using reported data by the world health organization for case studies of Italy and Iran. The numerical simulations and root mean square error criteria confirm the accuracy and efficiency of the findings of the present study.
{"title":"A simulation study of the COVID-19 pandemic based on the Ornstein-Uhlenbeck processes","authors":"P. Nabati","doi":"10.22034/CMDE.2021.43961.1864","DOIUrl":"https://doi.org/10.22034/CMDE.2021.43961.1864","url":null,"abstract":"The rapid spread of coronavirus disease (COVID-19) has increased the attention to the mathematical modeling of spreading the disease in the world. The behavior of spreading is not deterministic in the last year. The purpose of this paper is to presents a stochastic differential equation for modeling the data sets of the COVID-19 involving infected, recovered, and death cases. At first, the time series of the covid-19 is modeling with the Ornstein-Uhlenbeck process and then using the Ito lemma and Euler approximation the analytical and numerical simulations for the stochastic differential equation are achieved. Parameters estimation is done using the maximum likelihood estimator. Finally, numerical simulations are performed using reported data by the world health organization for case studies of Italy and Iran. The numerical simulations and root mean square error criteria confirm the accuracy and efficiency of the findings of the present study.","PeriodicalId":44352,"journal":{"name":"Computational Methods for Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2021-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48278102","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 : 2021-06-20DOI: 10.22034/CMDE.2021.39677.1736
Ahmed Bokhari, D. Baleanu, Rachid Belgacem
Prabhakar fractional operator was applied recently for studying the dynamics of complex systems from several branches of sciences and engineering. In this manuscript we discuss the regularized Prabhakar derivative applied to fractional partial differential equations using the Sumudu homotopy analysis method(PSHAM). Three illustrative examples are investigated to confirm our main results.
{"title":"Regularized Prabhakar Derivative Applications to Partial Differential Equations","authors":"Ahmed Bokhari, D. Baleanu, Rachid Belgacem","doi":"10.22034/CMDE.2021.39677.1736","DOIUrl":"https://doi.org/10.22034/CMDE.2021.39677.1736","url":null,"abstract":"Prabhakar fractional operator was applied recently for studying the dynamics of complex systems from several branches of sciences and engineering. In this manuscript we discuss the regularized Prabhakar derivative applied to fractional partial differential equations using the Sumudu homotopy analysis method(PSHAM). Three illustrative examples are investigated to confirm our main results.","PeriodicalId":44352,"journal":{"name":"Computational Methods for Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2021-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49179237","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 : 2021-06-20DOI: 10.22034/CMDE.2021.41166.1789
M. Woldaregay, H. Debela, G. Duressa
This paper deals with numerical treatment of singularly perturbed delay differential equations having delay on first derivative term. The solution of the considered problem exhibits boundary layer behaviour on left or right side of the domain depending on the sign of the convective term. The term with the delay is approximated using Taylor series approximation, resulting to asymptotically equivalent singularly perturbed boundary value problem. Uniformly convergent numerical scheme is developed using exponentially fitted finite difference method. The stability of the scheme is investigated using solution bound. The uniform convergence of the scheme is discussed and proved. Numerical examples are considered to validate the theoretical analysis.
{"title":"Uniformly convergent fitted operator method for singularly perturbed delay differential equations","authors":"M. Woldaregay, H. Debela, G. Duressa","doi":"10.22034/CMDE.2021.41166.1789","DOIUrl":"https://doi.org/10.22034/CMDE.2021.41166.1789","url":null,"abstract":"This paper deals with numerical treatment of singularly perturbed delay differential equations having delay on first derivative term. The solution of the considered problem exhibits boundary layer behaviour on left or right side of the domain depending on the sign of the convective term. The term with the delay is approximated using Taylor series approximation, resulting to asymptotically equivalent singularly perturbed boundary value problem. Uniformly convergent numerical scheme is developed using exponentially fitted finite difference method. The stability of the scheme is investigated using solution bound. The uniform convergence of the scheme is discussed and proved. Numerical examples are considered to validate the theoretical analysis.","PeriodicalId":44352,"journal":{"name":"Computational Methods for Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2021-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46116523","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 : 2021-06-20DOI: 10.22034/CMDE.2021.40288.1758
S. Abbasbandy, Hussein Sahihi, T. Allahviranloo
In this paper, a reliable new scheme is presented based on combining Reproducing Kernel Method (RKM) with a practical technique for the nonlinear problem to solve the System of Singularly Perturbed Boundary Value Problems (SSPBVP). The Gram-Schmidt orthogonalization process is removed in the present RKM. However, we provide error estimation for the approximate solution and its derivative. Based on the present algorithm in this paper, can also solve linear problem. Several numerical examples demonstrate that the present algorithm does have higher precision.
{"title":"Combining the reproducing kernel method with a practical technique to solve the system of nonlinear singularly perturbed boundary value problems","authors":"S. Abbasbandy, Hussein Sahihi, T. Allahviranloo","doi":"10.22034/CMDE.2021.40288.1758","DOIUrl":"https://doi.org/10.22034/CMDE.2021.40288.1758","url":null,"abstract":"In this paper, a reliable new scheme is presented based on combining Reproducing Kernel Method (RKM) with a practical technique for the nonlinear problem to solve the System of Singularly Perturbed Boundary Value Problems (SSPBVP). The Gram-Schmidt orthogonalization process is removed in the present RKM. However, we provide error estimation for the approximate solution and its derivative. Based on the present algorithm in this paper, can also solve linear problem. Several numerical examples demonstrate that the present algorithm does have higher precision.","PeriodicalId":44352,"journal":{"name":"Computational Methods for Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2021-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48446620","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 : 2021-06-14DOI: 10.22034/CMDE.2021.44736.1890
Asadollah Torabi Giklou, M. Ranjbar, M. Shafiee, V. Roomi
In this article, we use the collocation method based on the radial basis functions with sym- metric variable shape parameter (SVSP) to obtain numerical solutions of neutral-type functional- differential equations with proportional delays. We used Gaussian radial basis functions with SVSP. Using non uniform collocation points, we achieved a system and solving this system yielded the prob- lem solutions. Several examples are given to illustrate the efficiency and accuracy of the introduced method in comparison with the same method with the constant shape parameter (CSP) as well as other analytical and numerical methods. Comparison of the obtained numerical results shows the considerable superiority of the collocation method based on RBFs with SVSP in accuracy and convergence over the collocation method based on the RBFs with CSP and other analytical and numerical methods for delay differential equations (DDEs). Finally, numerical rate of convergence analysis of the numerical approximation was also obtained. It is observed that by comparing be- tween the obtained ROC values of error norms by the SVSP and CSP method, SVSP results were considered acceptable.
{"title":"Collocation method based on radial basis functions via symmetric variable shape parameter for solving a particular class of delay differential equations","authors":"Asadollah Torabi Giklou, M. Ranjbar, M. Shafiee, V. Roomi","doi":"10.22034/CMDE.2021.44736.1890","DOIUrl":"https://doi.org/10.22034/CMDE.2021.44736.1890","url":null,"abstract":"In this article, we use the collocation method based on the radial basis functions with sym- metric variable shape parameter (SVSP) to obtain numerical solutions of neutral-type functional- differential equations with proportional delays. We used Gaussian radial basis functions with SVSP. Using non uniform collocation points, we achieved a system and solving this system yielded the prob- lem solutions. Several examples are given to illustrate the efficiency and accuracy of the introduced method in comparison with the same method with the constant shape parameter (CSP) as well as other analytical and numerical methods. Comparison of the obtained numerical results shows the considerable superiority of the collocation method based on RBFs with SVSP in accuracy and convergence over the collocation method based on the RBFs with CSP and other analytical and numerical methods for delay differential equations (DDEs). Finally, numerical rate of convergence analysis of the numerical approximation was also obtained. It is observed that by comparing be- tween the obtained ROC values of error norms by the SVSP and CSP method, SVSP results were considered acceptable.","PeriodicalId":44352,"journal":{"name":"Computational Methods for Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2021-06-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44372192","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 : 2021-05-13DOI: 10.22034/CMDE.2021.22093.1257
M. Ramadan, Mohamed R. Ali
In this paper, we have proposed an efficient numerical method to solve a system linear fuzzy Fredholm integral equations of the second kind based on Bernoulli wavelet method (BWM). Bernoulli wavelets have been generated by dilation and translation of Bernoulli polynomials. The aim of this paper is to apply Bernoulli wavelet method to obtain approximate solutions of a system of linear fredholm fuzzy integral equations. First we introduce properties of Bernoulli wavelets then we used it to transform the integral equations to the system of algebraic equations, the error estimates of the proposed method is given and compared by solving some numerical examples.
{"title":"Bernoulli wavelet method for numerical solutions of system of fuzzy integral equations","authors":"M. Ramadan, Mohamed R. Ali","doi":"10.22034/CMDE.2021.22093.1257","DOIUrl":"https://doi.org/10.22034/CMDE.2021.22093.1257","url":null,"abstract":"In this paper, we have proposed an efficient numerical method to solve a system linear fuzzy Fredholm integral equations of the second kind based on Bernoulli wavelet method (BWM). Bernoulli wavelets have been generated by dilation and translation of Bernoulli polynomials. The aim of this paper is to apply Bernoulli wavelet method to obtain approximate solutions of a system of linear fredholm fuzzy integral equations. First we introduce properties of Bernoulli wavelets then we used it to transform the integral equations to the system of algebraic equations, the error estimates of the proposed method is given and compared by solving some numerical examples.","PeriodicalId":44352,"journal":{"name":"Computational Methods for Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2021-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48949984","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 : 2021-05-12DOI: 10.22034/CMDE.2021.44511.1885
M. Askari, H. Adibi
In this article, an efficient method for approximate the solution of the generalized Burgers-Huxley (gB-H) equation using multiquadric quasi-interpolation approach is considered. This method consists of two phases. First, the spatial derivatives are evaluated by MQ quasi-interpolation, So the gB-H equation is reduces to a nonlinear system of ordinary differential equations. In phase two, the obtained system is solved by using ODE solvers. Numerical examples demonstrate the validity and applicability of the method.
{"title":"Numerical investigation of the generalized Burgers-Huxley equation using combination of multiquadric quasi-interpolation and method of lines","authors":"M. Askari, H. Adibi","doi":"10.22034/CMDE.2021.44511.1885","DOIUrl":"https://doi.org/10.22034/CMDE.2021.44511.1885","url":null,"abstract":"In this article, an efficient method for approximate the solution of the generalized Burgers-Huxley (gB-H) equation using multiquadric quasi-interpolation approach is considered. This method consists of two phases. First, the spatial derivatives are evaluated by MQ quasi-interpolation, So the gB-H equation is reduces to a nonlinear system of ordinary differential equations. In phase two, the obtained system is solved by using ODE solvers. Numerical examples demonstrate the validity and applicability of the method.","PeriodicalId":44352,"journal":{"name":"Computational Methods for Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2021-05-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41997623","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 : 2021-05-09DOI: 10.22034/CMDE.2021.44459.1876
Yadollah AryaNejad
We examine the diffusion equation on the sphere. In this sense, we answer question of the symmetry classification. We provide the algebra of symmetry and build the optimal system of Lie subalgebras. We prove for one-dimensional optimal systems of Eq.(4), space is expanding Ricci solitons. Reductions of similarities related to subalgebras are classified, and some exact invariant solutions of the diffusion equation on the sphere are presented.
{"title":"Exact solutions of Diffusion Equation on sphere","authors":"Yadollah AryaNejad","doi":"10.22034/CMDE.2021.44459.1876","DOIUrl":"https://doi.org/10.22034/CMDE.2021.44459.1876","url":null,"abstract":"We examine the diffusion equation on the sphere. In this sense, we answer question of the symmetry classification. We provide the algebra of symmetry and build the optimal system of Lie subalgebras. We prove for one-dimensional optimal systems of Eq.(4), space is expanding Ricci solitons. Reductions of similarities related to subalgebras are classified, and some exact invariant solutions of the diffusion equation on the sphere are presented.","PeriodicalId":44352,"journal":{"name":"Computational Methods for Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2021-05-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44671074","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 : 2021-05-01DOI: 10.22034/CMDE.2021.44306.1873
I. T. Daba, G. Duressa
In this study, a robust computational method involving exponential cubic spline for solving singularly perturbed parabolic convection-diffusion equations arising in the modeling of neuronal variability has been presented. Some numerical examples are considered to validate the theoretical findings. The proposed scheme is shown to be an e-uniformly convergent accuracy of order O(Δt+h^2 ).
{"title":"A Robust computational method for singularly perturbed delay parabolic convection-diffusion equations arising in the modeling of neuronal variability","authors":"I. T. Daba, G. Duressa","doi":"10.22034/CMDE.2021.44306.1873","DOIUrl":"https://doi.org/10.22034/CMDE.2021.44306.1873","url":null,"abstract":"In this study, a robust computational method involving exponential cubic spline for solving singularly perturbed parabolic convection-diffusion equations arising in the modeling of neuronal variability has been presented. Some numerical examples are considered to validate the theoretical findings. The proposed scheme is shown to be an e-uniformly convergent accuracy of order O(Δt+h^2 ).","PeriodicalId":44352,"journal":{"name":"Computational Methods for Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2021-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46222899","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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