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Two-dimensional distributed order cable equation with non-singular kernel: a nonstandard implicit compact finite difference approach

Sweilam Nasser H., Ahmed Shimaa M., AL-Mekhlafi Seham M.

Journal of Applied Mathematics and Computational Mechanics

2024

Vol. 23, nr 2

93--104

In this work, a higher-order nonstandard implicit compact finite difference technique is used to study a two-dimensional nonlinear distributed order Cable problem. The distributed fractional order is defined in the Atangana-Baleanu sense. The key advantage of this strategy is the large stability areas it implicitly has. A particular focus is on examining the stability analysis of the proposed scheme through the application of the Jon Von Neumann approach. We show the effectiveness of the numerical scheme using two numerical examples, and we compare our results with the published literature to check the accuracy of the approach we have presented. The technique is a helpful tool for modeling this model, as demonstrated by the results.