Generalized Störmer–Cowell Methods for Nonlinear BVPs of Second-Order Delay-Integro-Differential Equations

Zhang, Chengjian; Cui, Li

doi:10.1007/s10915-017-0491-y

Cited by 9 publications

(1 citation statement)

References 20 publications

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“…Ghanbari and Kumar [18] studied a fractional predator-prey pathogen model, and the stability and convergence results wer obtained. Zhang and Li [19] proposed a numerical algorithm to solve a second-order-delay integro-differential equations based on the generalized Störmer-Cowell methods and compound quadrature rules.…”

Section: Definition 1 ([2-4])mentioning

confidence: 99%

Analysis of a High-Accuracy Numerical Method for Time-Fractional Integro-Differential Equations

2023

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A high-order finite difference numerical scheme based on the compact difference operator is proposed in this paper for time-fractional partial integro-differential equations with a weakly singular kernel, where the time-fractional derivative term is defined in the Riemann-Liouville sense. Here, the stability and convergence of the constructed compact finite difference scheme are proved in L∞ norm, with the accuracy order O(τ2+h4), where τ and h are temporal and spatial step sizes, respectively. The advantage of this numerical scheme is that arbitrary parameters can be applied to achieve the desired accuracy. Some numerical examples are presented to support the theoretical analysis.

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Section: Definition 1 ([2-4])mentioning

confidence: 99%

Analysis of a High-Accuracy Numerical Method for Time-Fractional Integro-Differential Equations

2023

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The adapted block boundary value methods for singular initial value problems

Wang

Zhang

2018

Calcolo

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Preconditioned quasi-compact boundary value methods for space-fractional diffusion equations

2019

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This paper focuses on highly-efficient numerical methods for solving spacefractional diffusion equations. By combining the fourth-order quasi-compact difference scheme and boundary value methods, a class of quasi-compact boundary value methods are constructed. In order to accelerate the convergence rate of this class of methods, the Kronecker product splitting (KPS) iteration method and the preconditioned method with KPS preconditioner are proposed. A convergence criterion for the KPS iteration method is derived. A numerical experiment further illustrates the computational efficiency and accuracy of the proposed methods. Moreover, a numerical comparison with the preconditioned method with Strang-type preconditioner is given, which shows that the preconditioned method with KPS preconditioner is comparable in computational efficiency.

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Generalized Störmer–Cowell Methods for Nonlinear BVPs of Second-Order Delay-Integro-Differential Equations

Cited by 9 publications

References 20 publications

Analysis of a High-Accuracy Numerical Method for Time-Fractional Integro-Differential Equations

Analysis of a High-Accuracy Numerical Method for Time-Fractional Integro-Differential Equations

The adapted block boundary value methods for singular initial value problems

Preconditioned quasi-compact boundary value methods for space-fractional diffusion equations

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