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An exact solution of the binary singular problem. (English) Zbl 1294.35034

Summary: Singularity problems exist in various branches of applied mathematics. Such ordinary differential equations accompany singular coefficients. In this paper, by using the properties of reproducing kernel, the exact solution expressions of dual singular problems are given in the reproducing kernel space and studied, also for a class of singular problems. For the binary equation of singular points, we put it into the singular problem first, and then reuse some excellent properties which are applied to solve the method of solving differential equations for its exact solution expression of binary singular integral equation in reproducing kernel space, and then obtain its approximate solution through the evaluation of exact solutions. Numerical examples show the effectiveness of this method.

MSC:

35J75 Singular elliptic equations
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