A new class of exponential propagation iterative methods of Runge-Kutta type (EPIRK)

Tokman M.

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A new class of exponential propagation iterative methods of Runge-Kutta type (EPIRK)

机译：Runge-Kutta类型（EPIRK）的一类新的指数传播迭代方法

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We propose a new class of the exponential propagation iterative methods of Runge-Kutta-type (EPIRK). The EPIRK schemes are exponential integrators that can be competitive with explicit and implicit methods for integration of large stiff systems of ODEs. Introducing the new, more general than previously proposed, ansatz for EPIRK schemes allows for more flexibility in deriving computationally efficient high-order integrators. Recent extension of the theory of B-series to exponential integrators [1] is used to derive classical order conditions for schemes up to order five. An algorithm to systematically solve these conditions is presented and several new fifth order schemes are constructed. Several numerical examples are used to verify the order of the methods and to illustrate the performance of the new schemes.

机译：我们提出了一类新的Runge-Kutta型（EPIRK）的指数传播迭代方法。 EPIRK方案是指数积分器，可以与用于大型刚性ODE系统的显式和隐式方法进行竞争。为EPIRK方案引入新的，比以前提议的更通用的ansatz，可以在推导计算效率高的高阶积分器时提供更大的灵活性。 B系列理论对指数积分器[1]的最新扩展用于推导最多五阶方案的经典阶条件。提出了一种系统地解决这些条件的算法，并构建了几种新的五阶方案。几个数值示例用于验证方法的顺序并说明新方案的性能。

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《Journal of Computational Physics》 |2011年第24期|共17页
作者
Tokman M.;
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正文语种 eng
中图分类数学物理方法;
关键词
B-series; Exponential integrators; Exponential propagation iterative (EPI) methods; Krylov projections; Large scale computing; Newton-Krylov implicit methods; Order conditions; Stiff systems;

机译：B系列;指数积分器;指数传播迭代（EPI）方法;Krylov投影;大规模计算;Newton-Krylov隐式方法;阶数条件;刚性系统;

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1. A new class of exponential propagation iterative methods of Runge-Kutta type (EPIRK) [J] . Tokman M. Journal of Computational Physics . 2011,第24期

机译：Runge-Kutta类型（EPIRK）的一类新的指数传播迭代方法
2. Generalized Picard iterations: A class of iterated Runge-Kutta methods for stiff problems [J] . Boris Faleichik, Ivan Bondar, Vasily Byl Journal of Computational and Applied Mathematics . 2014,第Null期

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3. Parallel iterated methods based on variable step-size multistep Runge-Kutta methods of Radau type for stiff problems [J] . K. Burrage, H. Suhartanto Advances in computational mathematics . 2000,第3期

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A new class of exponential propagation iterative methods of Runge-Kutta type (EPIRK)

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