Spline-interpolation solution of a plane Stefan problem

Document Type : Research Article

Author

Pyotr Ivanshin

Kazan National Research Technical University, Kazan, Russia

10.22067/ijnao.2025.94508.1683

Abstract

We construct a spline-interpolation solution of the 2D Stefan problem. We reduce it to the set of boundary value problems for analytic functions and integral equations. Our construction of an approximate solution is based on construction of analytic functions and application of approximate solutions of boundary-value problems. We modify the initial problem in order to reduce it to the set of boundary value problems. The first of the problems that arises here is the Cauchy problem for Laplace equation. The second problem is the Riemann problem for analytic function, We also give estimates of the approximate solution error and some examples of the solution.

Keywords

Spline

Analytic function

Approximate solution

Cauchy problem

Subjects

• Numerical methods for differential equations and its applications

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