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Local radial basis function-finite difference based algorithms for singularly perturbed Burgers’ model

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  • Jiwari, Ram

Abstract

This work analyzes singularly perturbed Burgers’ model by developing two meshfree algorithms based on local radial basis function-finite difference approximation. The main goal of this task is to present computational modeling of the model when perturbation parameter ɛ→0 where most of the traditional numerical methods fail. In the evolvement of the first algorithm, time derivative is discretized by forward finite difference and then truncation error, stability and convergence analysis are discussed for the semi-discrete model. After that, local radial basis function-finite difference approximation is used for spatial discretization. In the second numerical algorithm, local radial basis function-finite difference and RK4 method are applied for spatial and fully discretization respectively. Also, the stability of the scheme is discussed via matrix method.

Suggested Citation

  • Jiwari, Ram, 2022. "Local radial basis function-finite difference based algorithms for singularly perturbed Burgers’ model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 198(C), pages 106-126.
    • Handle: RePEc:eee:matcom:v:198:y:2022:i:c:p:106-126
    DOI: 10.1016/j.matcom.2022.02.024
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    References listed on IDEAS

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    1. Oruç, Ömer, 2021. "A radial basis function finite difference (RBF-FD) method for numerical simulation of interaction of high and low frequency waves: Zakharov–Rubenchik equations," Applied Mathematics and Computation, Elsevier, vol. 394(C).
    2. Saka, Bülent & Dağ, İdris, 2007. "Quartic B-spline collocation method to the numerical solutions of the Burgers’ equation," Chaos, Solitons & Fractals, Elsevier, vol. 32(3), pages 1125-1137.
    3. Mingzhu Li & Lijuan Chen & Qiang Ma, 2014. "A Meshfree Quasi-Interpolation Method for Solving Burgers’ Equation," Mathematical Problems in Engineering, Hindawi, vol. 2014, pages 1-8, July.
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    Cited by:

    1. Zhang, Yuhui & Rabczuk, Timon & Lin, Ji & Lu, Jun & Chen, C.S., 2024. "Numerical simulations of two-dimensional incompressible Navier-Stokes equations by the backward substitution projection method," Applied Mathematics and Computation, Elsevier, vol. 466(C).
    2. Cao, Baiheng & Wu, Xuedong & Wang, Yaonan & Zhu, Zhiyu, 2024. "Modified hybrid B-spline estimation based on spatial regulator tensor network for burger equation with nonlinear fractional calculus," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 220(C), pages 253-275.
    3. Cheng Chi & Fajie Wang & Lin Qiu, 2023. "A Novel Coupled Meshless Model for Simulation of Acoustic Wave Propagation in Infinite Domain Containing Multiple Heterogeneous Media," Mathematics, MDPI, vol. 11(8), pages 1-15, April.

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