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    A Simple, Fast, and Accurate Time-Integrator for Strongly Nonlinear Dynamical Systems

    T.A. Elgohary1,2, L. Dong3, J.L. Junkins2,4, S.N. Atluri1,4

    CMES-Computer Modeling in Engineering & Sciences, Vol.100, No.3, pp. 249-275, 2014, DOI:10.3970/cmes.2014.100.249

    Abstract In this study, we consider Initial Value Problems (IVPs) for strongly nonlinear dynamical systems, and study numerical methods to analyze short as well as long-term responses. Dynamical systems characterized by a system of second-order nonlinear ordinary differential equations (ODEs) are recast into a system of nonlinear first order ODEs in mixed variables of positions as well as velocities. For each discrete-time interval Radial Basis Functions (RBFs) are assumed as trial functions for the mixed variables in the time domain. A simple collocation method is developed in the time-domain, with Legendre-Gauss-Lobatto nodes as RBF source points as well as collocation points.… More >

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