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On Some Finite Difference Schemes for the Solutions of Parabolic Partial Differential Equations

This paper presents the comparison of three different and unique finite difference schemes used for finding the solutions of parabolic partial differential equations (PPDE). Knowing fully that the efficiency of a numerical schemes depends solely on their stability therefore, the schemes were compared based on their stability using von Newmann method. The implicit scheme and Dufort-Frankel schemes using von Newmann stability method are unconditionally stable, while the explicit scheme is conditionally stable. The schemes were also applied to solve a one dimensional parabolic partial differential equations (heat equation) numerically and their results compared for best in efficiency. The numerical experiments as seen in the tables presented and also the percentage errors, which proves that the implicit scheme is good compare to the other two schemes. Also, the implementation of the implicit scheme is faster than that of the explicit and Dufort-Frankel schemes. The results obtained in work also compliment and agrees with the results in literature.

Finite Difference Schemes, Stability, Von Newmann Method, Accuracy, Heat Equation

Omowo Babajide Johnson, Longe Idowu Oluwaseun, Osakwe Charles Nnamdi. (2023). On Some Finite Difference Schemes for the Solutions of Parabolic Partial Differential Equations. International Journal of Systems Science and Applied Mathematics, 8(1), 1-6.

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