Advanced numerical treatment of modified Burger’s equations using method of lines and cubic B-splines

The modified Burger’s equation is a nonlinear partial differential equation that has numerous applications across physics and engineering. This paper presents a numerical solution approach by combining the method of lines and cubic B-Spline interpolation for the modified Burger’s equation. By discre...

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Bibliographic Details
Main Authors: Muhammad Yaseen, Irsa Ashraf, Aziz Khan, Thabet Abdeljawad
Format: Article
Language:English
Published: Elsevier 2025-06-01
Series:Results in Control and Optimization
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Online Access:http://www.sciencedirect.com/science/article/pii/S2666720725000475
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Summary:The modified Burger’s equation is a nonlinear partial differential equation that has numerous applications across physics and engineering. This paper presents a numerical solution approach by combining the method of lines and cubic B-Spline interpolation for the modified Burger’s equation. By discretizing the spatial domain into grid points via the cubic B-splines, the given PDE is transformed into a system of ordinary differential equations (ODEs), facilitating approximation of the solution. The resulting ODE system is then numerically solved via the fourth-order Runge–Kutta method. Stability and convergence analyses of the scheme are also conducted. A comprehensive numerical analysis of the scheme with a comparison against previously published results in the literature is presented. This study enriches the field of computational mathematics by exploring cubic B-spline interpolation within the context of the method of lines for solving both linear and nonlinear partial differential equations.
ISSN:2666-7207