10.57647/mathsci.2025.1901.03

High-Order Combined Compact Finite Difference Method to Solve Partial Differential Equations

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  • Hamid Emamifar1,
  • Majid Tavassoli Kajani*1,
  1. Department of Mathematics, Isf. C., Islamic Azad University, Isfahan, Iran

Received: 2025-01-28

Revised: 2025-03-13

Accepted: 2025-03-21

Published in Issue 2025-03-31

Published Online: 2025-03-21

Copyright (c) 2025 H. Emamifar, Majid Tavassoli Kajani (Author)

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

Emamifar, H., & Tavassoli Kajani, M. (2025). High-Order Combined Compact Finite Difference Method to Solve Partial Differential Equations. Mathematical Sciences, 19(1 (March 2025). https://doi.org/10.57647/mathsci.2025.1901.03
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Abstract

In this study, we introduce an 8th-order combined compact finite difference (CCD) method for solving partial dif-ferential equations (PDEs). By employing the 8th-order CCD approach to discretize spatial derivatives, we transform PDEs into a system of ordinary differential equations (ODEs). We then apply the RK(8)7 method to solve these ODEs efficiently. Our analysis demonstrates the convergence of this technique and highlights its accuracy through various numerical examples. These findings indicate the potential of the proposed high-order CCD method for delivering precise solutions to complex PDEs, making it a valuable tool for numerical analysis and a wide range of applications.

Keywords

  • Combined compact finite difference method,
  • Runge-Kuttamethod,
  • partial differential equations,
  • stability
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