An Efficient Exponential Integrator for Large Nonlinear Stiff Systems Part 2: Symplecticity and Global Error Analysis
Paper in proceedings, 2014
In the first part of this study an exponential integration scheme for computing solutions of large stiff systems was presented. It was claimed that the integrator is particularly efficient in large-scale problems with localized nonlinearity when compared to general-purpose methods. Theoretical aspects of the proposed method were investigated. The method computational efficiency was increased by using an approximation of the Jacobian matrix. This was achieved by combining the proposed integration scheme with the developed methods for model reduction, in order to treat the large nonlinear problems. In this second part geometric and structural properties of the presented integration algorithm are examined and preservation of these properties such as area in the phase plane and also energy consistency are investigated. The error analysis is given through small scale examples and the efficiency and accuracy of the proposed exponential integrator is investigated through a large-scale size problem that originates from a moving load problem in railway mechanics. The superiority of the proposed method in sense of computational efficiency, for large-scale problems particularly system with localized nonlinearity, has been demonstrated, comparing the results with classical Runge–Kutta approach.