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首页> 外文会议>International Symposium on Symbolic and Algebraic Computation Aug 3-6, 2003 Philadelphia, Pennsylvania, USA >Computing Power Series Solutions of a Nonlinear PDE System
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Computing Power Series Solutions of a Nonlinear PDE System

机译：计算非线性PDE系统的幂级数解

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摘要

This paper presents a new algorithm to compute the power series solutions of a significant class of nonlinear systems of partial differential equations. The algorithm is very different from previous algorithms to perform this task. Those relie on differentiating iteratively the differential equations to get coefficients of the power series, one at a time. The algorithm presented here relies on using the linearisation of the system and the associated recurrences. At each step the order up to which the power series solution is known is doubled. The algorithm can be seen as belonging to the family of Newton iteration methods.
机译：本文提出了一种新的算法来计算一类重要的偏微分方程非线性系统的幂级数解。该算法与执行此任务的先前算法有很大不同。那些依靠迭代微分方程来一次获得幂级数的系数。这里介绍的算法依赖于使用系统的线性化和相关的递归。在每个步骤中，已知幂级数解决方案的顺序都会加倍。该算法可以视为属于牛顿迭代方法族。

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