Improving stability domains of the implicit higher order accuracy method

• Published in: International journal for numerical methods in engineering Vol. 88; no. 9; pp. 880 - 896
• Main Authors: Rezaiee-Pajand, M., Sarafrazi, S. R., Hashemian, M.
• Format: Journal Article
• Language: English
• Published: Chichester, UK John Wiley & Sons, Ltd 02.12.2011; Wiley
• Subjects: Accuracy; Dispersions; Exact sciences and technology; Extrapolation; implicit higher order accuracy process; improving stability; Mathematical models; Mathematics; nonlinear dynamic analysis; Numerical analysis; Numerical analysis. Scientific computation; numerical time integration; Optimization; Partial differential equations, initial value problems and time-dependant initial-boundary value problems; Sciences and techniques of general use; Stability; Strategy; Time integration; improving stability; Numerical integration; implicit higher order accuracy process; numerical time integration; nonlinear dynamic analysis; Non linear effect; Time integration; Dispersion; Optimization; Numerical stability
• ISSN: 0029-5981; 1097-0207; 1097-0207
• DOI: 10.1002/nme.3204

The implicit higher order accuracy (IHOA) time integration family has a high order of accuracy. However, its stability domains are very restrictive. By improving the stability conditions, the larger time steps can be utilized. In this study, two parameters are introduced in the displacement and velocity extrapolations of IHOA. In order to find the optimum values of the proposed parameters, the dissipation and the dispersion are investigated. Three conditionally stable versions of the second‐, third‐, and forth‐order algorithms are found. It is shown that these formulations have larger stability domains than the previous ones. Furthermore, the suggested strategies give responses that are more accurate. Copyright © 2011 John Wiley & Sons, Ltd.