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On the Convergence and Stability of Finite Difference Method for Parabolic Partial Differential Equations

  • B. J. Omowo
  • I. O. Longe
  • C. E. Abhulimen
  • H. K. Oduwole

Journal of Advances in Mathematics and Computer Science, Page 58-67
DOI: 10.9734/jamcs/2021/v36i1030412
Published: 21 December 2021

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Abstract


In this paper, we verify the convergence and stability of implicit (modified) finite difference scheme. Knowing fully that consistency and stability are very important criteria for convergence, we have prove the stability of the modied implicit scheme using the von Newmann method and also verify the convergence by comparing the numerical solution with the exact solution. The results shows that the schemes converges even as the step size is rened.


Keywords:
  • Finite difference scheme
  • Crank-Nicolson scheme
  • stability
  • modifed Crank-Nicolson scheme
  • diffusion equations.
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How to Cite

Omowo, B. J., Longe, I. O., Abhulimen, C. E., & Oduwole, H. K. (2021). On the Convergence and Stability of Finite Difference Method for Parabolic Partial Differential Equations. Journal of Advances in Mathematics and Computer Science, 36(10), 58-67. https://doi.org/10.9734/jamcs/2021/v36i1030412
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References

Abhulimen CE, Omowo BJ. Modied Crank-Nicolson method for solving one dimensional parabolic equation. International Journal of Scientic Research. 2019;15(6)series 3:60-66

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Omowo BJ, Abhulimen CE. On the stability of Modied Crank-Nicolson method for Parabolic Partial dierential equations. International Journal of Mathematical Sciences and Optimization: Theory and Application. 2021;6(2):862-873.

Omowo Babajide Johnson, Longe Idowu Oluwaseun. Crank-Nicolson and Modied Crank- Nicolson scheme for one dimensional parabolic partial dierential equation. International journal of Applied Mathematics and Theoretical Physics. 2020;6(3):35-40.

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Qiqi Tran, Jinjie Lin. Modied Iterated Crank-Nicolson method with improved Accuracy. arXiv: 1608.01344 V1 [math.NA].

Simeon Kiprono Mariton. Modied Crank Nicholson Based Methods on the Solution of one dimensional Heat Equation. Nonlinear Analysis and Dierential Equations. 2019;7(1):33-37.

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