Nonequidistant modified predictor-corrector methods for solving systems of differential equations

Abstract

This paper shows that it is possible to develop nonequidistant predictor-corrector formulae with minimum error bounds for solving systems of differential equations such that the tedious difficulties which arise in practical applications can be overcome. General predictor-corrector formulae with variable steps are constructed. Explicit third order- and fourth order-two points formulae are derived. Also fourth order-three points formulae are represented. Two theorems are given. A flow chart for general nonequidistant predictor-corrector methods using automatic control for the step length is compactly represented for solving systems of differential equations. These methods are recommended to be used widely in practice because of many advantages.

Keywords:

• Predictor
• modifier
• corrector
• final value
• truncation error
• round off troubles
• minimum error bounds
• margin of stability
• norm of matrix.

C.R. Categories:

• 5.17