Numerical time integration for dynamic analysis using a new higher order predictor-corrector method

• Published in: Engineering computations Vol. 25; no. 6; pp. 541 - 568
• Main Authors: Rezaiee-Pajand, M., Alamatian, J.
• Format: Journal Article
• Language: English
• Published: Bradford Emerald Group Publishing Limited 01.01.2008
• Subjects: Accuracy; Algorithms; Computer aided software engineering; Dynamical systems; Efficiency; Equilibrium; Integration; Methods; Numerical analysis; Studies; Velocity; Predictor-corrector methods; Structures; Numerical analysis
• ISSN: 0264-4401; 1758-7077
• DOI: 10.1108/02644400810891544

Purpose - This paper aims to provide a simple and accurate higher order predictor-corrector integration which can be used in dynamic analysis and to compare it with the previous works.Design methodology approach - The predictor-corrector integration is defined by combining the higher order explicit and implicit integrations in which displacement and velocity are assumed to be functions of accelerations of several previous time steps. By studying the accuracy and stability conditions, the weighted factors and acceptable time step are determined.Findings - Simplicity and vector operations plus accuracy and stability are the main specifications of the new predictor-corrector method. This procedure can be used in linear and nonlinear dynamic analysis.Research limitations implications - In the proposed integration, time step is assumed to be constant.Practical implications - The numerical integration is the heart of a dynamic analysis. The result's accuracy is strongly influenced by the accuracy and stability of the numerical integration.Originality value - This paper presents simple and accurate predictor-corrector integration based on accelerations of several previous time steps. This may be used as a routine in any dynamic analysis software to enhance accuracy and reduce computational time.