A numerical solution of the dissipative wave equation by means of the cubic B-spline method

• Published in: Journal of physics communications 2021-10, Vol.5 (10), p.105014
• Main Authors: Alaofi, Z M, Ali, T S, Dragomir, S S
• Format: Article
• Language: English
• Subjects: Accuracy; cubic B-spline polynomial; nonlinear dissipative wave equation; Partial differential equations; Von Neumann stability analysis
• ISSN: 2399-6528; 2399-6528
• DOI: 10.1088/2399-6528/ac2940

In the past few decades, partial differential equations have drawn considerable attention, owing to their ability to model certain physical phenomena. The aim of this paper is to investigate a cubic B-spline polynomial to obtain a numerical solution of a nonlinear dissipative wave equation. For the numerical procedure, the time derivative is obtained by the usual finite difference scheme. The approximate solution and its principal derivatives over the subinterval is approximated by the combination of the cubic B-spline and unknown element parameters. The accuracy of the proposed method will be shown by computing L∞ error norms for different time levels. By applying Von Neumann stability analysis, the developed method is shown to be conditionally stable for given values of specified parameters. A numerical example is given to illustrate the accuracy of the cubic B-spline polynomial method. The obtained numerical results show that our proposed method maintains good accuracy.