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

Abstract

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.