使用伪解析形式幂求解平面中二阶椭圆算子的边值和特征值问题
Solution of boundary value and eigenvalue problems for second order elliptic operators in the plane using pseudoanalytic formal powers
AI总结：
提出一种利用伪解析函数理论（特别是伪解析形式幂）构造算子D=div p grad + q的完整零解系统，并通过递归积分算法求解有界单连通区域上的边值和谱问题。
摘要：
我们提出了一种使用伪解析函数理论，特别是伪解析形式幂，求解平面中椭圆算子D=div p grad + q的边值和特征值问题的方法。在系数p和q满足一定条件下，借助伪解析函数理论，可以通过一个由递归积分组成的简单算法构造算子的完整零解系统。该解系统用于求解有界单连通区域中算子D的边值和谱问题。我们研究了该方法的理论和数值方面。
英文摘要：
We propose a method for solving boundary value and eigenvalue problems for the elliptic operator D=divpgrad+q in the plane using pseudoanalytic function theory and in particular pseudoanalytic formal powers. Under certain conditions on the coefficients p and q with the aid of pseudoanalytic function theory a complete system of null solutions of the operator can be constructed following a simple algorithm consisting in recursive integration. This system of solutions is used for solving boundary value and spectral problems for the operator D in bounded simply connected domains. We study theoretical and numerical aspects of the method.
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