El Numerical approximation to the Dirichlet problem for the Poisson equation in half lens domain

Authors

Diego Toala Maestría en Matemática, Facultad de Posgrado, Universidad Técnica de Manabí, Manabí, Ecuador. https://orcid.org/0000-0001-7628-8651
Judith Vanegas Vicerrectorado Académico, Universidad Yachay Tech, Urcuquí, Ecuador. https://orcid.org/0000-0003-0748-5963

DOI:

https://doi.org/10.33936/revbasdelaciencia.v10i2.7544

Keywords:

Dirichlet boundary value problem, half lens domain, Poisson’s equation, numerical approximation.

Abstract

This work presents an approximate solution to the Dirichlet problem for the two-dimensional Poisson equation in a half lens domain. Based on the Green’s function specific to this domain, a particular solution was derived through the integral representation of the problem. Subsequently, a numerical approach was implemented in MATLAB to evaluate this integral representation. The numerical results, presented in tables and plots, demonstrate the method’s performance using metrics such as execution time. This solution represents a first step toward future numerical implementations using fast algorithms, including the Fast Fourier Transform.

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