The error of Euler's method for floating-point arithmetic computations

E. A. Kalinina, O. N. Samarina

Saint-Petersburg State University, Saint-Petersburg, RUSSIA

Abstract: We present an algorithm that enables us to find the optimal number of steps in Euler's method, in the sense of computational precision, while solving a Cauchy problem for a system of linear differential equations with constant coefficients. We include numerical examples of applications of this method for evaluating a solution to the Cauchy problem at a point and constructing solutions to systems of nonlinear ordinary differential equations.

Keywords: Euler's method, Cauchy problem, system of ordinary differential equations, floating-point arithmetic, computational error.

UDC: 519.622.2

Received: 30.11.2009
Revised: 12.04.2011

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