Pub Date : 2021-10-25DOI: 10.22034/CMDE.2021.46473.1953
S. Kumbinarasaiah, P. PreethamM.
This paper generated the novel approach called the Clique polynomial method (CPM) using the Clique polynomials raised in graph theory. Non-linear initial value problems are converted into non-linear algebraic equations by discretion with suitable grid points in the current approach. We solved highly non-linear initial problems using the (HAM) Homotopy analysis method and CPM. Obtained results reveal that the present technique is better than HAM that is discussed through tables and simulations. Convergence analyses are reflected in terms of the theorem.
{"title":"A Study on Homotopy Analysis Method and Clique Polynomial Method","authors":"S. Kumbinarasaiah, P. PreethamM.","doi":"10.22034/CMDE.2021.46473.1953","DOIUrl":"https://doi.org/10.22034/CMDE.2021.46473.1953","url":null,"abstract":"This paper generated the novel approach called the Clique polynomial method (CPM) using the Clique polynomials raised in graph theory. Non-linear initial value problems are converted into non-linear algebraic equations by discretion with suitable grid points in the current approach. We solved highly non-linear initial problems using the (HAM) Homotopy analysis method and CPM. Obtained results reveal that the present technique is better than HAM that is discussed through tables and simulations. Convergence analyses are reflected in terms of the theorem.","PeriodicalId":44352,"journal":{"name":"Computational Methods for Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2021-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47960623","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 : 2021-10-25DOI: 10.22034/CMDE.2021.46753.1964
T. Mathanaranjan
In the present study, we investigate the conformable space-time fractional cubic-quartic nonlinear Schrodinger equation with three different laws of nonlinearity namely, parabolic law, quadratic-cubic law, and weak non-local law.This model governs the propagation of solitons through nonlinear optical fibers. An effective approach namely, the exp(-Pi(xi))-expansion method is applied to construct some new exact solutions of the governing model. Consequently, the dark, singular, rational and periodic solitary wave solutions are successfully revealed. The comparisons with other results are also presented. In addition, the dynamical structures of obtained solutions are presented through 3D and 2D plots.
{"title":"An effective technique for the conformable space-time fractional cubic-quartic nonlinear Schrodinger equation with different laws of nonlinearity","authors":"T. Mathanaranjan","doi":"10.22034/CMDE.2021.46753.1964","DOIUrl":"https://doi.org/10.22034/CMDE.2021.46753.1964","url":null,"abstract":"In the present study, we investigate the conformable space-time fractional cubic-quartic nonlinear Schrodinger equation with three different laws of nonlinearity namely, parabolic law, quadratic-cubic law, and weak non-local law.This model governs the propagation of solitons through nonlinear optical fibers. An effective approach namely, the exp(-Pi(xi))-expansion method is applied to construct some new exact solutions of the governing model. Consequently, the dark, singular, rational and periodic solitary wave solutions are successfully revealed. The comparisons with other results are also presented. In addition, the dynamical structures of obtained solutions are presented through 3D and 2D plots.","PeriodicalId":44352,"journal":{"name":"Computational Methods for Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2021-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42416010","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 : 2021-10-25DOI: 10.22034/CMDE.2021.45950.1927
Z. Abdollahy, Y. Mahmoudi, A. S. Shamloo, M. Baghmisheh
In this study, one explicit and one implicit finite differencescheme is introduced for the numerical solution of time-fractionalRiesz space diffusion equation. The time derivative is approximatedby the standard Gr"{u}nwald Letnikov formula of order one, whilethe Riesz space derivative is discretized by Fourier transform-basedalgorithm of order four. The stability and convergence of theproposed methods are studied. It is proved that the implicit schemeis unconditionally stable, while the explicit scheme is stableconditionally. Some examples are solved to illustrate the efficiencyand accuracy of the proposed methods. Numerical results confirm thatthe accuracy of present schemes is of order one.
{"title":"Two explicit and implicit finite difference schemes for time fractional Riesz space diffusion equation","authors":"Z. Abdollahy, Y. Mahmoudi, A. S. Shamloo, M. Baghmisheh","doi":"10.22034/CMDE.2021.45950.1927","DOIUrl":"https://doi.org/10.22034/CMDE.2021.45950.1927","url":null,"abstract":"In this study, one explicit and one implicit finite differencescheme is introduced for the numerical solution of time-fractionalRiesz space diffusion equation. The time derivative is approximatedby the standard Gr\"{u}nwald Letnikov formula of order one, whilethe Riesz space derivative is discretized by Fourier transform-basedalgorithm of order four. The stability and convergence of theproposed methods are studied. It is proved that the implicit schemeis unconditionally stable, while the explicit scheme is stableconditionally. Some examples are solved to illustrate the efficiencyand accuracy of the proposed methods. Numerical results confirm thatthe accuracy of present schemes is of order one.","PeriodicalId":44352,"journal":{"name":"Computational Methods for Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2021-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41545797","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 : 2021-08-13DOI: 10.22034/CMDE.2021.44502.1879
Anteneh Getachew Gebrie, Dejene Shewakena Bedane
Based on the extragradient-like method combined with shrinking projection, we propose two algorithms, the first algorithm is obtained using sequential computation of extragradientlike method and the second algorithm is obtained using parallel computation of extragradient-like method, to find a common point of the set of fixed points of nonexpansive mapping and the solution set of the equilibrium problem of a bifunction given as a sum of finite number of H¨older continuous bifunctions. The convergence theorems for iterative sequences generated by the algorithms are established under widely used assumptions for the bifunction and its summands.
{"title":"Hybrid shrinking projection extragradient-like algorithms for equilibrium and fixed point problems","authors":"Anteneh Getachew Gebrie, Dejene Shewakena Bedane","doi":"10.22034/CMDE.2021.44502.1879","DOIUrl":"https://doi.org/10.22034/CMDE.2021.44502.1879","url":null,"abstract":"Based on the extragradient-like method combined with shrinking projection, we propose two algorithms, the first algorithm is obtained using sequential computation of extragradientlike method and the second algorithm is obtained using parallel computation of extragradient-like method, to find a common point of the set of fixed points of nonexpansive mapping and the solution set of the equilibrium problem of a bifunction given as a sum of finite number of H¨older continuous bifunctions. The convergence theorems for iterative sequences generated by the algorithms are established under widely used assumptions for the bifunction and its summands.","PeriodicalId":44352,"journal":{"name":"Computational Methods for Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2021-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45194782","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 : 2021-08-08DOI: 10.22034/CMDE.2021.45176.1903
A. Yokuş, K. Ali, R. Yilmazer, H. Bulut
In the current study, we consider the generalized Pochhammer-Chree equation with term of order $n$. Based on the (1/G')-expansion method and with the aid of symbolic computation, we construct some distinct exact solutions for this nonlinear model. Various exact solutions are produced to the studied equation including singular solutions, periodic wave solutions. In addition to 2D, 3D and contour plots are graphed for all obtaining solutions via choosing the suitable values for the involved parameters. All gained solutions verify the governing equation.
{"title":"On exact solutions of the generalized Pochhammer-Chree equation","authors":"A. Yokuş, K. Ali, R. Yilmazer, H. Bulut","doi":"10.22034/CMDE.2021.45176.1903","DOIUrl":"https://doi.org/10.22034/CMDE.2021.45176.1903","url":null,"abstract":"In the current study, we consider the generalized Pochhammer-Chree equation with term of order $n$. Based on the (1/G')-expansion method and with the aid of symbolic computation, we construct some distinct exact solutions for this nonlinear model. Various exact solutions are produced to the studied equation including singular solutions, periodic wave solutions. In addition to 2D, 3D and contour plots are graphed for all obtaining solutions via choosing the suitable values for the involved parameters. All gained solutions verify the governing equation.","PeriodicalId":44352,"journal":{"name":"Computational Methods for Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2021-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48548655","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 : 2021-08-08DOI: 10.22034/CMDE.2021.44619.1881
R. Memarbashi, A. Ghasemabadi, Z. Ebadi
Among the various causes of heroin addiction, the use of prescription opioids is one of the main reasons. In this article, we introduce and analyze a two strain epidemic model with super infection for modeling the effect of prescribed opioids abuse on heroin addiction. Our model contains the effect of relapse of individuals under treatment/rehabilitation to drug abuse in each strain. We extract the basic reproductive ratio, the invasion numbers, and study the occurrence of backward bifurcation in strain dominance equilibria, i.e., boundary equilibria. Also, we study both local and global stability of DFE and boundary equilibria under suitable conditions. Furthermore, we study the existence of the coexistence equilibrium point. We prove that when $R_0<1$, the coexistence equilibrium point can exist, i.e., backward bifurcation occurs in coexistence equilibria. Finally, we use numerical simulation to describe the obtained analytical results.
{"title":"Backward bifurcation in a two strain model of heroin addiction","authors":"R. Memarbashi, A. Ghasemabadi, Z. Ebadi","doi":"10.22034/CMDE.2021.44619.1881","DOIUrl":"https://doi.org/10.22034/CMDE.2021.44619.1881","url":null,"abstract":"Among the various causes of heroin addiction, the use of prescription opioids is one of the main reasons. In this article, we introduce and analyze a two strain epidemic model with super infection for modeling the effect of prescribed opioids abuse on heroin addiction. Our model contains the effect of relapse of individuals under treatment/rehabilitation to drug abuse in each strain. We extract the basic reproductive ratio, the invasion numbers, and study the occurrence of backward bifurcation in strain dominance equilibria, i.e., boundary equilibria. Also, we study both local and global stability of DFE and boundary equilibria under suitable conditions. Furthermore, we study the existence of the coexistence equilibrium point. We prove that when $R_0<1$, the coexistence equilibrium point can exist, i.e., backward bifurcation occurs in coexistence equilibria. Finally, we use numerical simulation to describe the obtained analytical results.","PeriodicalId":44352,"journal":{"name":"Computational Methods for Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2021-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44682899","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 : 2021-08-08DOI: 10.22034/CMDE.2021.42440.1829
Sepideh Niknam, H. Adibi
In this research, linear combination of moving least square (MLS) and local radial basis functions(LRBFs)is considered within the framework of meshless method to solve two-dimensional hyperbolic telegraph equation.Besides, differential quadrature method (DQM) is employed to discretize temporal derivatives. Furthermore, a control parameter is introduced and optimized to achieve minimum errors via an experimental approach.Illustrative examples are provided to demonstrate applicability and efficiency of the method. The results prove the superiority of this method overusing MLS and LRBF individually.
{"title":"A numerical solution of two-dimensional hyperbolic telegraph equation based on moving least square meshless method and radial basis functions","authors":"Sepideh Niknam, H. Adibi","doi":"10.22034/CMDE.2021.42440.1829","DOIUrl":"https://doi.org/10.22034/CMDE.2021.42440.1829","url":null,"abstract":"In this research, linear combination of moving least square (MLS) and local radial basis functions(LRBFs)is considered within the framework of meshless method to solve two-dimensional hyperbolic telegraph equation.Besides, differential quadrature method (DQM) is employed to discretize temporal derivatives. Furthermore, a control parameter is introduced and optimized to achieve minimum errors via an experimental approach.Illustrative examples are provided to demonstrate applicability and efficiency of the method. The results prove the superiority of this method overusing MLS and LRBF individually.","PeriodicalId":44352,"journal":{"name":"Computational Methods for Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2021-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41584070","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 : 2021-08-08DOI: 10.22034/CMDE.2021.45436.1911
F. Alizadeh, M. S. Hashemi, A. Badali
In this work, we use the symmetry of the Lie group analysis as one of the powerful tools which that deals with the wide class of fractional order differential equation in the Riemann-Liouville concept. We employ the classical Lie symmetries to obtain similarity reductions of nonlinear time-fractional Benjamin-Ono equation and then, we find the related exact solutions for the derived generators. Finally, according to the Lie symmetry generators obtained, we construct conservation laws for related classical vector fields of time-fractional Benjamin-Ono equation.
{"title":"Lie symmetries, exact solutions, and conservation laws of the nonlinear time-fractional Benjamin-Ono equation","authors":"F. Alizadeh, M. S. Hashemi, A. Badali","doi":"10.22034/CMDE.2021.45436.1911","DOIUrl":"https://doi.org/10.22034/CMDE.2021.45436.1911","url":null,"abstract":"In this work, we use the symmetry of the Lie group analysis as one of the powerful tools which that deals with the wide class of fractional order differential equation in the Riemann-Liouville concept. We employ the classical Lie symmetries to obtain similarity reductions of nonlinear time-fractional Benjamin-Ono equation and then, we find the related exact solutions for the derived generators. Finally, according to the Lie symmetry generators obtained, we construct conservation laws for related classical vector fields of time-fractional Benjamin-Ono equation.","PeriodicalId":44352,"journal":{"name":"Computational Methods for Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2021-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43603033","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 : 2021-08-08DOI: 10.22034/CMDE.2021.44790.1891
H. Mesgarani, S. Ahanj, Y. E. Aghdam
A novel local meshless scheme based on the radial basis function (RBF) is introduced in this article for price multi-asset options of even European and American types based on the Black-Scholes model. The proposed approach is obtained by using operator splitting and repeating the schemes of Richardson extrapolation in the time direction and coupling the RBF technology with a finite-difference (FD) method that leads to extremely sparse matrices in the spatial direction. Therefore, it is free of the ill-conditioned difficulties that are typical of the standard RBF approximation. We have used a strong iterative idea named the stabilized Bi-conjugate gradient process (BiCGSTAB) to solve highly sparse systems raised by the new approach. Moreover, based on a review performed in the current study, the presented scheme is unconditionally stable in the case of independent assets when spatial discretization nodes are equispaced. As seen in numerical experiments, it has a low computational cost and generates higher accuracy. Finally, the proposed local RBF scheme is very versatile so that it can be used easily for Solving numerous models and obstacles not just in the finance sector, as well as in other fields of engineering and science. Finally, we conclude that the proposed local RBF scheme is very versatile so that it can be used easily for Solving numerous models and obstacles not just in the finance sector, as well as in other fields of engineering and science.
{"title":"A novel local meshless scheme based on the radial basis function for pricing multi-asset options","authors":"H. Mesgarani, S. Ahanj, Y. E. Aghdam","doi":"10.22034/CMDE.2021.44790.1891","DOIUrl":"https://doi.org/10.22034/CMDE.2021.44790.1891","url":null,"abstract":"A novel local meshless scheme based on the radial basis function (RBF) is introduced in this article for price multi-asset options of even European and American types based on the Black-Scholes model. The proposed approach is obtained by using operator splitting and repeating the schemes of Richardson extrapolation in the time direction and coupling the RBF technology with a finite-difference (FD) method that leads to extremely sparse matrices in the spatial direction. Therefore, it is free of the ill-conditioned difficulties that are typical of the standard RBF approximation. We have used a strong iterative idea named the stabilized Bi-conjugate gradient process (BiCGSTAB) to solve highly sparse systems raised by the new approach. Moreover, based on a review performed in the current study, the presented scheme is unconditionally stable in the case of independent assets when spatial discretization nodes are equispaced. As seen in numerical experiments, it has a low computational cost and generates higher accuracy. Finally, the proposed local RBF scheme is very versatile so that it can be used easily for Solving numerous models and obstacles not just in the finance sector, as well as in other fields of engineering and science. Finally, we conclude that the proposed local RBF scheme is very versatile so that it can be used easily for Solving numerous models and obstacles not just in the finance sector, as well as in other fields of engineering and science.","PeriodicalId":44352,"journal":{"name":"Computational Methods for Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2021-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48023043","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 : 2021-06-30DOI: 10.22034/CMDE.2021.42554.1832
A. Golmankhaneh, K. Ali, R. Yilmazer, Mohammed K. A. Kaabar
In this manuscript, we review fractal calculus and the analogues of both local Fourier transform with its related properties and Fourier convolution theorem are proposed with proofs in fractal calculus. The fractal Dirac delta with its derivative and the fractal Fourier transform of the Dirac delta are also defined. In addition, some important applications of the local fractal Fourier transform are presented in this paper such as the fractal electric current in a simple circuit, the fractal second order ordinary differential equation, and the fractal Bernoulli-Euler beam equation. All discussed applications are closely related to the fact that, in fractal calculus, a useful local fractal derivative is a generalized local derivative in the standard calculus sense. In addition, a comparative analysis is also carried out to explain the benefits of this fractal calculus parameter on the basis of the additional alpha parameter, which is the dimension of the fractal set, such that when $alpha=1$, we obtain the same results in the standard calculus.
{"title":"Local Fractal Fourier Transform and Applications","authors":"A. Golmankhaneh, K. Ali, R. Yilmazer, Mohammed K. A. Kaabar","doi":"10.22034/CMDE.2021.42554.1832","DOIUrl":"https://doi.org/10.22034/CMDE.2021.42554.1832","url":null,"abstract":"In this manuscript, we review fractal calculus and the analogues of both local Fourier transform with its related properties and Fourier convolution theorem are proposed with proofs in fractal calculus. The fractal Dirac delta with its derivative and the fractal Fourier transform of the Dirac delta are also defined. In addition, some important applications of the local fractal Fourier transform are presented in this paper such as the fractal electric current in a simple circuit, the fractal second order ordinary differential equation, and the fractal Bernoulli-Euler beam equation. All discussed applications are closely related to the fact that, in fractal calculus, a useful local fractal derivative is a generalized local derivative in the standard calculus sense. In addition, a comparative analysis is also carried out to explain the benefits of this fractal calculus parameter on the basis of the additional alpha parameter, which is the dimension of the fractal set, such that when $alpha=1$, we obtain the same results in the standard calculus.","PeriodicalId":44352,"journal":{"name":"Computational Methods for Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2021-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42873387","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：