A New High Order Accurate, Finite Difference Method on Quasi-variable Meshes for the Numerical Solution of Three Dimensional Poisson Equation

Abstract

In this paper, a compact high order accurate finite difference scheme on non-uniform meshes network to solve the 3D Poisson equation is presented. We considered here the development of classical Numerov’s method in combination with nonuniform quasi-variable meshes network. The theoretical validation of the present scheme is considered by means of irreducibility and monotonicity criteria of the coefficient matrix obtained from difference equations. Numerical tests are presented to validate the theoretical prediction of the proposed scheme.

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Acknowledgements

We are thankful to reviewers for their useful comments and suggestions. The author also acknowledges to Dr. Ritesh Kumar Dubey for the partial support through project from DST-SERB, New Delhi, India under Grant no. EMR/2016/000394/MS.

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Correspondence to Neelesh Kumar.

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The author acknowledges to Dr. Ritesh Kumar Dubey for the partial support through project from DST-SERB, New Delhi, India under Grant no. EMR/2016/000394/MS.

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Kumar, N. A New High Order Accurate, Finite Difference Method on Quasi-variable Meshes for the Numerical Solution of Three Dimensional Poisson Equation. Differ Equ Dyn Syst 29, 21–34 (2021). https://doi.org/10.1007/s12591-019-00475-x

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Keywords

  • Finite difference methods
  • Quasi-variable meshes
  • Poisson equation
  • High order methods
  • Nonuniform meshes

Mathematics Subject Classification

  • 65N06
  • 35J25
  • 65N12