A DISCUSSION ON EULER METHOD: A REVIEW Vol. 1(2) July 2013, No. 16, pp. 294-317 B. N. BISWAS, S. CHATTERJEE, S. P. MUKHERJEE AND S. PAL

Abstract

Notwithstanding the efforts of earlier workers some fundamental aspects of an introductory course on numerical methods have been overlooked.This paper dwells on this aspect.It is sometimes felt that the step size is root cause for such misconceptions.But it is hardly felt that clubbing of the forward Euler algorithm with the backward Euler algorithm for convenience can lead to serious misconceptions and of course it depends on the nature of the problems.With this in mind we consider few such problems that falls under the category of Ordinary Differential Equation (ODE), a differential equation containing one or more derivatives of the dependent variable.However nothing is discussed on the error due to nesting of forward Euler method in backward Euler method.It is shown in this paper that there is a maximum value of step size up to which the numerical algorithms are stable.This tutorial paper attempt to illustrate these issues by taking some practical example that has exact analytical solutions, so that pitfalls of the numerical algorithm can be vividly illustrated.Moreover, the discussion of linear systems offers considerable insight into the solution of non-linear equations.