Fourth-order two-stage explicit exponential integrators for time-dependent PDEs

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• 作者：Vu Thai Luan^a ; ^b ; ^{vluan@ucmerced.edu}
• 关键词：Exponential integrators ; Exponential Rosenbrock methods ; Nonstiff problems ; Stiff problems ; Superconvergence
• 刊名：Applied Numerical Mathematics
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：112
• 期：Complete
• 页码：91-103
• 全文大小：501 K
• 卷排序：112

文摘

Among the family of fourth-order time integration schemes, the two-stage Gauss–Legendre method, which is an implicit Runge–Kutta method based on collocation, is the only superconvergent. The computational cost of this implicit scheme for large systems, however, is very high since it requires solving a nonlinear system at every step. Surprisingly, in this work we show that one can construct and prove convergence results for exponential methods of order four which use two stages only. Specifically, we derive two new fourth-order two-stage exponential Rosenbrock schemes for solving large systems of differential equations. Moreover, since the newly schemes are not only superconvergent but also fully explicit, they turn out to be very competitive compared to the two-stage Gauss–Legendre method as well as other fourth-order time integration schemes. Numerical experiments are given to demonstrate the efficiency of the new integrators.