Numerical Study of One-Phase Stefan-Type Problems

Document Type : Research Paper

Authors

Department of Applied Mathematics‎, ‎University of Tabriz‎, ‎Iran

10.22052/ijmc.2025.255182.1881

Abstract

‎We all know that parabolic equations with non-classical boundary conditions and Stefan's problem have become very popular in recent years due to their many applications in more basic and applied science problems‎. ‎Also‎, ‎differential equations with integral conditions have found wide applications in solving chemistry and physics problems‎. ‎Many problems that appear in heat transfer can be reduced to non-classical problems with integral conditions‎.
‎In this document‎, ‎we first mention the application of Stefan's one-phase problems‎, ‎including the non-classical thermal equation and the integral boundary condition‎, ‎in problems related to chemistry‎. ‎Then we examine a numerical technique to solve it and prove the convergence of the method‎.
‎Finally‎, ‎numerical examples are presented to demonstrate the effectiveness of the method for solving linear and nonlinear diffusion-response equations with these non-classical conditions‎.

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References

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Iranian Journal of Mathematical Chemistry
Volume 16, Issue 2
In Progress
June 2025
Pages 127-139

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