Far East Journal of Applied Mathematics

The Far East Journal of Applied Mathematics publishes original research papers and survey articles in applied mathematics, covering topics such as nonlinear dynamics, approximation theory, and mathematical modeling. It encourages papers focusing on algorithm development.

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A NUMERICAL PROCEDURE THROUGH THE METHOD OF LINES ADDRESSING A GINZBURG-LANDAU TYPE EQUATION ON A NON-CIRCULAR TYPE DOMAIN IN THE CONTEXT OF POLAR AND CARTESIAN COORDINATES

Authors

  • Fabio Silva Botelho

Keywords:

generalized method of lines, polar coordinates, non-circular domain shape, finite differences approach, numerical optimization

DOI:

https://doi.org/10.17654/0972096025007

Abstract

This article develops a method for obtaining an approximate solution for a Ginzburg-Landau type partial differential equation through an application of the generalized method of lines. More specifically, we address the issue of setting a boundary condition on a non-circular domain boundary, in the context of polar and Cartesian coordinates.

Received: May 11, 2025
Accepted: July 14, 2025

References

J. F. Annet, Superconductivity, superfluids and condensates, 2nd ed., Oxford Master Series in Condensed Matter Physics, Oxford University Press, Reprint, 2010.

L. D. Landau and E. M. Lifschits, Course of Theoretical Physics, Vol. 5, Statistical Physics, Part 1, Butterworth-Heinemann, Elsevier, Reprint, 2008.

F. S. Botelho, An approximate proximal numerical procedure concerning the generalized method of lines, Mathematics 10(16) (2022), 2950.

https://doi.org/10.3390/math10162950.

F. S. Botelho, Functional Analysis, Calculus of Variations and Numerical Methods for Models in Physics and Engineering, CRC Taylor and Francis, Florida, 2020.

R. A. Adams and J. F. Fournier, Sobolev Spaces, 2nd ed., Elsevier, New York, 2003.

J. C. Strikwerda, Finite Difference Schemes and Partial Differential Equations, SIAM, 2nd ed., Philadelphia, 2004.

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Published

2025-07-19

Issue

Vol. 118 No. 2 (2025)

Section

Articles

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How to Cite

A NUMERICAL PROCEDURE THROUGH THE METHOD OF LINES ADDRESSING A GINZBURG-LANDAU TYPE EQUATION ON A NON-CIRCULAR TYPE DOMAIN IN THE CONTEXT OF POLAR AND CARTESIAN COORDINATES. (2025). Far East Journal of Applied Mathematics, 118(2), 119-130. https://doi.org/10.17654/0972096025007

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