Solution of initial value problems using ndsolve of mathematica

Abstract

In the paper, the hyperbolic equations of the form (1) are approximated by the semi-finite difference schemes O(h2) and O(h4) accurate. The resulting two stiff systems of ordinary differential equations with initial conditions are solved by a Mathematica modules utilizing the function NDSolve. The stiffness ratios of the differential equations are evaluated. For the purpose of illustration of the method, two examples have been solved and the numerical and graphical results are given.

Keywords: Finite difference method, stiffness ratio.