Comparative Analysis of Schemes with Movable Nodes for a Parabolic Equation

Authors

  • Dalabaev Umurdin Department of System Analysis and Mathematical Modeling, University of World Economy and Diplomacy, Tashkent, Uzbekistan
  • Xasanova Dilfuza Department of System Analysis and Mathematical Modeling, University of World Economy and Diplomacy, Tashkent, Uzbekistan

DOI:

https://doi.org/10.14738/aivp.126.17966

Keywords:

parabolic equation, approximate-analytical solution, moving nodes

Abstract

The article considers an approximate analytical solution of a linear parabolic equation with initial and boundary conditions. Many problems in engineering applications are reduced to solving an initial-boundary value problem of parabolic type. There are various analytical, approximate-analytical and numerical methods for solving such problems. The most popular difference methods for solving an initial-boundary value problem of a parabolic equation are explicit, implicit and Crank-Nicolson schemes. Here, we consider methods for obtaining an approximate-analytical solution based on the movable node method and their comparative analysis of these schemes for specific test problems. A comparison of the exact and approximate solutions is made using specific examples.

References

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Published

2024-12-25

How to Cite

Umurdin, D., & Dilfuza, X. (2024). Comparative Analysis of Schemes with Movable Nodes for a Parabolic Equation. European Journal of Applied Sciences, 12(06), 344–352. https://doi.org/10.14738/aivp.126.17966

Issue

Vol. 12 No. 06 (2024): European Journal of Applied Sciences

Section

Articles

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Copyright (c) 2024 Dalabaev Umurdin, Xasanova Dilfuza

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This work is licensed under a Creative Commons Attribution 4.0 International License.