Convergence analysis of the hp-version spectral collocation method for a class of nonlinear variable-order fractional differential equations

Yan, Rian; Ma, Qiang; Ding, Xiaohua

doi:10.1016/j.apnum.2021.05.013

Cited by 2 publications

(3 citation statements)

References 34 publications

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“…The use of rational approximation (24) resolves the issues of computing matrix exponential functions and computing matrix inverses A −1 and A −3 but it creates another issue of computing matrix polynomial inverses (6I + (3 + √ 3)kA) −2 and (12I + (3 + √ 3)kA) −2 . This is handled by applying splitting techniques, as follows:…”

Section: Split Version Of the New Methodsmentioning

confidence: 99%

“…The shifted Vieta-Lucas polynomials are used to build a numerical scheme. The authors of [24] derived the numerical scheme based on hp-version spectral collocation methods of the variableorder fractional approach. Based on a natural generalization of the classic Riesz potential, Darve et al [25] developed a unique definition of the variable-order fractional Laplacian on R n .…”

Section: Introductionmentioning

confidence: 99%

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Highly Efficient Numerical Algorithm for Nonlinear Space Variable-Order Fractional Reaction–Diffusion Models

Yousuf,

Sarwar

2023

Fractal Fract

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In this paper, we present a new highly efficient numerical algorithm for nonlinear variable-order space fractional reaction–diffusion equations. The algorithm is based on a new method developed by using the Gaussian quadrature pole rational approximation. A splitting technique is used to address the issues related to computational efficiency and the stability of the method. Two linear systems need to be solved using the same real-valued discretization matrix. The stability and convergence of the method are discussed analytically and demonstrated through numerical experiments by solving test problems from the literature. The variable-order diffusion effects on the solution profiles are illustrated through graphs. Finally, numerical experiments demonstrate the superiority of the presented method in terms of computational efficiency, accuracy, and reliability.

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Section: Split Version Of the New Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Highly Efficient Numerical Algorithm for Nonlinear Space Variable-Order Fractional Reaction–Diffusion Models

Yousuf,

Sarwar

2023

Fractal Fract

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show abstract

“…The shiftediVieta-Lucasipolynomials are used to build a numerical scheme. The authors [41] derived the numerical scheme based on hp-versionispectral collocationi methods variable-order fractional approach. Based on a natural generalization of the classic Riesz potential, Darve et al [4] developed a unique definition of variable-order fractional Laplacian on R n .…”

Section: Introductionmentioning

confidence: 99%

Highly efficient numerical algorithm for nonlinear space variable order fractional reaction-diffusion models

Yousuf

Sarwar

2023

Preprint

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In this paper, we present a new novel highly efficient numerical method for non-linear variable order space fractional reaction-diffusion equations. The method is developed using Gaussian quadrature pole rational approximation instead of Padé rational approximation to avoid complex arithmetic. Issues related to computational efficiency and stability of the method are addressed using partial fraction decomposition technique and an easy to implement algorithm is developed. Two linear systems are required to be solved with the same real-valued discretization matrix. The stability and convergence of the method is discussed analytically and demonstrated through numerical experiments by solving some test problems from the literature. The effects of variable order diffusion on the solution profiles are illustrated through graphs. Finally, numerical experiments demonstrate the superiority of the presented method in terms of computational efficiency, accuracy, and reliability. MSC Classification: 26A33 , 35K57 , 65M12

show abstract

Convergence analysis of the hp-version spectral collocation method for a class of nonlinear variable-order fractional differential equations

Cited by 2 publications

References 34 publications

Highly Efficient Numerical Algorithm for Nonlinear Space Variable-Order Fractional Reaction–Diffusion Models

Highly Efficient Numerical Algorithm for Nonlinear Space Variable-Order Fractional Reaction–Diffusion Models

Highly efficient numerical algorithm for nonlinear space variable order fractional reaction-diffusion models

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