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<p>We construct approximate solutions of the 2D Cauchy problem for domains bounded by nonsmooth curves. We reduce these solutions to the set of boundary value problems for analytic functions and integral equations. Our construction of an approximate solution is based on introduction of analytic functions and application of approximate conformal mappings. We reduce the initial problem to the set of boundary value problems and systems of linear algebraic equations. We also give estimates of the approximate solution error and some examples of the solution.</p>

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Approximate Solution of Cauchy Problem for a Harmonic Function in a Domain with Corners

  • 期刊论文

  • 发表日期：

    2026年6月1日

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  • P. N. Ivanshin

摘要

We construct approximate solutions of the 2D Cauchy problem for domains bounded by nonsmooth curves. We reduce these solutions to the set of boundary value problems for analytic functions and integral equations. Our construction of an approximate solution is based on introduction of analytic functions and application of approximate conformal mappings. We reduce the initial problem to the set of boundary value problems and systems of linear algebraic equations. We also give estimates of the approximate solution error and some examples of the solution.