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A Bivariate Spectral Linear Partition Method for Solving Nonlinear Evolution Equations
  • Fezile Bangetile Khumalo,
  • Sandile Motsa,
  • Vusi Magagula
Fezile Bangetile Khumalo
University of Eswatini Faculty of Science and Engineering

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Sandile Motsa
University of Eswatini Faculty of Science and Engineering
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Vusi Magagula
University of Eswatini Faculty of Science and Engineering
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This work develops a method for solving nonlinear evolution equations. The method, termed a bivariate spectral linear partition method, BSLPM, combines the Chebyshev spectral collocation method, bivariate Lagrange interpolation, and a linear partition technique as an underlying linearization method. It is developed for an n th order nonlinear differential equation and then used to solve three known evolution problems. The results are compared with known exact solutions from literature. The method’s applicability, reliability, and accuracy are confirmed by the congruence between the numerical and exact solutions. Tables, error graphs, and convergence graphs were generated using MATLAB (R2015a), to confirm the order of accuracy of the method and verify its convergence. The performance of the method is also observed against other methods performing well in these types of differential equations and is found to be comparable in terms of accuracy. The proposed method is also efficient as it uses minimal computation time.
02 May 2023Submitted to Mathematical Methods in the Applied Sciences
14 May 2023Assigned to Editor
14 May 2023Submission Checks Completed
20 May 2023Review(s) Completed, Editorial Evaluation Pending
21 May 2023Reviewer(s) Assigned
13 Nov 2023Editorial Decision: Revise Minor
19 Nov 20231st Revision Received