Variable Step-Size Selection Methods for Implicit Integration Schemes

摘要

Implicit integration schemes are widely used in mathematics and engineering to solve ordinary differential equations. Every integration method requires one to choose a step-size for the independent variable which affects the efficiency and accuracy of the scheme. As every implicit integration scheme has a global error inherent to the scheme, we choose the total number of computations in order to achieve a prescribed global error as a measure of efficiency. A systematic method for choosing step-size is presented which is based on minimizing an efficiency function. The approach is applied to two popular numerical integration schemes.