khalid Karam Ali
Mathematics Department, Faculty of Science, Al-Azhar University, Nasr City (11884), Cairo, Egypt
[ 1 ] - Numerical studies of non-local hyperbolic partial differential equations using collocation methods
The non-local hyperbolic partial differential equations have many applications in sciences and engineering. A collocation finite element approach based on exponential cubic B-spline and quintic B-spline are presented for the numerical solution of the wave equation subject to nonlocal boundary condition. Von Neumann stability analysis is used to analyze the proposed methods. The efficiency, accu...
[ 2 ] - Application of linear combination between cubic B-spline collocation methods with different basis for solving the KdV equation
In the present article, a numerical method is proposed for the numerical solution of the KdV equation by using a new approach by combining cubic B-spline functions. In this paper we convert the KdV equation to system of two equations. The method is shown to be unconditionally stable using von-Neumann technique. To test accuracy the error norms L2, L∞ are computed. Three invariants of motion are...
[ 3 ] - Non-polynomial Spline Method for Solving Coupled Burgers Equations
In this paper, non-polynomial spline method for solving Coupled Burgers Equations are presented. We take a new spline function. The stability analysis using Von-Neumann technique shows the scheme is unconditionally stable. To test accuracy the error norms 2L, L are computed and give two examples to illustrate the sufficiency of the method for solving such nonlinear partial differential equation...
Co-Authors