通过边值问题数值计算Evans函数
Computing Evans functions numerically via boundary-value problems
AI总结：
本文提出一种基于边值问题的数值计算Evans函数方法，证明了算法收敛性，并展示了多维问题的特征值计算示例，方法具有线性可扩展性。
摘要：
Evans函数已被广泛用于研究空间扩展偏微分方程中行波解的谱稳定性。为了数值计算Evans函数，已开发出几种射线方法。本文提出了一种替代方案，该方案依赖于适当边界值问题的公式化。证明了该算法的收敛性，并给出了几个例子，包括多维问题的特征值计算。与早期方法相比，所提出方案的主要优势是该方案是线性的，并且可扩展到大规模问题。
英文摘要：
The Evans function has been used extensively to study spectral stability of travelling-wave solutions in spatially extended partial differential equations. To compute Evans functions numerically, several shooting methods have been developed. In this paper, an alternative scheme for the numerical computation of Evans functions is presented that relies on an appropriate boundary-value problem formulation. Convergence of the algorithm is proved, and several examples, including the computation of eigenvalues for a multi-dimensional problem, are given. The main advantage of the scheme proposed here compared with earlier methods is that the scheme is linear and scalable to large problems.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
