Abstract
In this Research Method of Line is used to find the approximation solution of one dimensional singularly perturbed Burger equation given with initial and boundary conditions. First, the given solution domain is discretized and the derivative involving the spatial variable x is replaced into the functional values at each grid points by using the central finite difference method. Then, the resulting first-order linear ordinary differential equation is solved by the fifth-order Runge-Kutta method. To validate the applicability of the proposed method, one model example is considered and solved for different values of the perturbation parameter ‘ ’ and mesh sizes in the direction of the temporal variable, t. Numerical results are presented in tables in terms of Maximum point-wise error, N t , E and rate of convergence, N t , P . The stability of this new class of Numerical method is also investigated by using Von Neumann stability analysis techniques. The numerical results presented in tables and graphs confirm that the approximate solution is in good agreement with the exact solution.
Highlights
Numerical analysis is a subject that involves computational methods for studying and solving mathematical problems
It’s widely used by scientists and engineers to solve some problems. Such problems may be formulated in terms of an algebraic equation, transcendental equations, ordinary differential equations, and partial differential equations [1], [3]
Numerical analysis is concerned with the theoretical foundation of numerical algorithms for the solution of problems arising in scientific applications [3]
Summary
Numerical analysis is a subject that involves computational methods for studying and solving mathematical problems. It is a branch of mathematics and computer science that creates, analyzes, and implements algorithms for solving mathematical problems numerically [2]. It’s widely used by scientists and engineers to solve some problems. Such problems may be formulated in terms of an algebraic equation, transcendental equations, ordinary differential equations, and partial differential equations [1], [3]. Numerical analysis is concerned with the theoretical foundation of numerical algorithms for the solution of problems arising in scientific applications [3]. Include modeling mechanical vibration, heat, sound vibration, elasticity, and fluid dynamics [16]
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