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A novel meshless space-time backward substitution method and its application to nonhomogeneous advection-diffusion problems

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  • Lin, Ji
  • Zhang, Yuhui
  • Reutskiy, Sergiy
  • Feng, Wenjie

Abstract

For time-dependent problems, a novel space-time backward substitution method is proposed in this paper. By employing the space-time radial basis function and the space-time trigonometric basis function in the original backward substitution method, the space-time backward substitution method is obtained. Compared with the traditional backward substitution method, this novel numerical method avoids the time-difference measurement in the temporal approximation, which may result in accumulative errors, and at the same time maintains the existing advantages. Furthermore, the proposed method can be easily used to solve more general time-dependent problems. To evaluate the accuracy and efficiency, several numerical examples are tested and compared.

Suggested Citation

  • Lin, Ji & Zhang, Yuhui & Reutskiy, Sergiy & Feng, Wenjie, 2021. "A novel meshless space-time backward substitution method and its application to nonhomogeneous advection-diffusion problems," Applied Mathematics and Computation, Elsevier, vol. 398(C).
    • Handle: RePEc:eee:apmaco:v:398:y:2021:i:c:s0096300321000126
    DOI: 10.1016/j.amc.2021.125964
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    References listed on IDEAS

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    1. Fuzhang Wang & Enran Hou & Imtiaz Ahmad, 2020. "A Direct Meshless Method for Solving Two-Dimensional Second-Order Hyperbolic Telegraph Equations," Journal of Mathematics, Hindawi, vol. 2020, pages 1-9, November.
    2. Wang, Dan & Chen, C.S. & Fan, C.M. & Li, Ming, 2019. "The MAPS based on trigonometric basis functions for solving elliptic partial differential equations with variable coefficients and Cauchy–Navier equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 159(C), pages 119-135.
    3. Lin, Ji & Reutskiy, S.Y. & Lu, Jun, 2018. "A novel meshless method for fully nonlinear advection–diffusion-reaction problems to model transfer in anisotropic media," Applied Mathematics and Computation, Elsevier, vol. 339(C), pages 459-476.
    4. Lin, Ji & Reutskiy, Sergiy, 2020. "A cubic B-spline semi-analytical algorithm for simulation of 3D steady-state convection-diffusion-reaction problems," Applied Mathematics and Computation, Elsevier, vol. 371(C).
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    Cited by:

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    2. Li, Yancheng & Liu, Cong & Li, Wei & Chai, Yingbin, 2023. "Numerical investigation of the element-free Galerkin method (EFGM) with appropriate temporal discretization techniques for transient wave propagation problems," Applied Mathematics and Computation, Elsevier, vol. 442(C).
    3. Yingbin Chai & Kangye Huang & Shangpan Wang & Zhichao Xiang & Guanjun Zhang, 2023. "The Extrinsic Enriched Finite Element Method with Appropriate Enrichment Functions for the Helmholtz Equation," Mathematics, MDPI, vol. 11(7), pages 1-25, March.
    4. Xunbai Du & Sina Dang & Yuzheng Yang & Yingbin Chai, 2022. "The Finite Element Method with High-Order Enrichment Functions for Elastodynamic Analysis," Mathematics, MDPI, vol. 10(23), pages 1-27, December.
    5. 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).
    6. Sina Dang & Gang Wang & Yingbin Chai, 2023. "A Novel “Finite Element-Meshfree” Triangular Element Based on Partition of Unity for Acoustic Propagation Problems," Mathematics, MDPI, vol. 11(11), pages 1-21, May.
    7. Tingting Sun & Peng Wang & Guanjun Zhang & Yingbin Chai, 2022. "A Modified Radial Point Interpolation Method (M-RPIM) for Free Vibration Analysis of Two-Dimensional Solids," Mathematics, MDPI, vol. 10(16), pages 1-20, August.
    8. Sun, Fengxin & Wang, Jufeng & Xu, Ying, 2024. "An improved stabilized element-free Galerkin method for solving steady Stokes flow problems," Applied Mathematics and Computation, Elsevier, vol. 463(C).
    9. Jue Qu & Hongjun Xue & Yancheng Li & Yingbin Chai, 2022. "An Enriched Finite Element Method with Appropriate Interpolation Cover Functions for Transient Wave Propagation Dynamic Problems," Mathematics, MDPI, vol. 10(9), pages 1-12, April.

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