Stability and dispersion analysis of reproducing kernel collocation method for transient dynamics

• Published in: Applied mathematics and mechanics Vol. 32; no. 6; pp. 777 - 788
• Main Author: 罗汉中 刘学文 黄醒春
• Format: Journal Article
• Language: English
• Published: Heidelberg Shanghai University Press 01.06.2011; School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiao Tong University,Shanghai 200240, P. R. China%Siemens Industry Software China Co., Ltd., 14F, Cloud-9 Office Tower, No. 1018,Changning Road, Shanghai 200042, P. R. China
• Subjects: Accuracy; Algorithms; Applications of Mathematics; Classical Mechanics; Collocation methods; Dynamic tests; Dynamics; Fluid- and Aerodynamics; Kernels; Mathematical Modeling and Industrial Mathematics; Mathematical models; Mathematics; Mathematics and Statistics; Partial Differential Equations; Stability; transient dynamics; O302; reproducing kernel collocation method (RKCM); 65M12; stability analysis; dispersion analysis
• ISSN: 0253-4827; 1573-2754
• DOI: 10.1007/s10483-011-1457-6

A reproducing kernel collocation method based on strong formulation is introduced for transient dynamics. To study the stability property of this method, an algorithm based on the von Neumann hypothesis is proposed to predict the critical time step. A numerical test is conducted to validate the algorithm. The numerical critical time step and the predicted critical time step are in good agreement. The results are compared with those obtained based on the radial basis collocation method, and they axe in good agreement. Several important conclusions for choosing a proper support size of the reproducing kernel shape function are given to improve the stability condition.