Spline collocation methods for solving some types of nonlinear parabolic partial differential equations

Volume 31, Issue 3, pp 262--273 http://dx.doi.org/10.22436/jmcs.031.03.03

Publication Date: May 12, 2023 Submission Date: January 16, 2023 Revision Date: March 29, 2023 Accteptance Date: April 05, 2023

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Authors

B. A. Mahmood - Department of Mathematics, College of Science, University of Duhok, Duhok, Iraq. S. A. Tahir - Department of Mathematics, College of Science, University of Sulaiumai, Sulaiumai, Iraq. K. H. F. Jwamer - Department of Mathematics, College of Science, University of Sulaiumai, Sulaiumai, Iraq.

Abstract

In this work, some types of nonlinear parabolic partial differential equations have been studied by means of the collocation method with cubic B-splines, without transformation or linearization. Here, the convergence analysis of the current scheme is also theoretically investigated. A few numerical examples are given to illustrate the viability and effectiveness of the proposed technique. The error norms \(l_2\) and \(l_{\infty}\) are used to assess the accuracy of the current method. In this respect, the proposed method, keeping the real features of such problems, is able to save the behavior of nonlinear terms without facing any conventional drawbacks. Furthermore, it is mathematically shown and numerically seen that there is a good agreement between the approximation and the exact solutions. The current approach reduces the cost of calculation as well as the need for storage space at various parameters.

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Keywords

• Cubic B-spline
• collocation method
• numerical solution
• SSP-RK54 scheme
• nonlinear partial differential equations

MSC

•  35Q35
•  80M25
•  33F05
•  34K28

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