Numerical method for the solution of integral equations in a problem with directional derivative for the Laplace equation outside open curvesстатья
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Дата последнего поиска статьи во внешних источниках: 19 декабря 2016 г.
Аннотация:By using a simple layer potential and an angular potential, one can reduce the
problem with a directional derivative for the Laplace equation outside several open curves on
the plane to a uniquely solvable system of integral equations that consists of an integral equation
of the second kind and additional integral conditions. The kernel in the integral equation of
the second kind contains singularities and can be represented as a Cauchy singular integral.
We suggest a numerical method for solving a system of integral equations. Quadrature formulas
for the logarithmic and angular potentials are represented. The quadrature formula for the
logarithmic potential preserves the property of its continuity across the boundary (open curves).