Accuracy Estimation of numerical methods of the analysis of the relaxation oscillator

 

A. M. Pilipenko, V. N. Biryukov

Southern Federal University

The paper is received on November 6, 2013

Abstract. In the paper the modern numerical methods for solving ordinary differential equations are testing. These methods are widely applied in simulators of RF circuits. As a test problem the relaxation oscillator’s differential equation with arbitrary polygonal nonlinearity was selected. An estimation of accuracy of numerical methods is received in the case of simulation of the relaxation oscillator. It is shown that the error of solution is determined by the methodological error and random errors caused by 1) an error of synchronization of the numerical solutions with the period of oscillation, 2) changes in the current step.

Keywords: numerical methods, nonlinear differential equations, relaxation oscillator, error analysis.