Abstract
In this paper, we investigate the closed-form particular solutions of Poisson’s equation using the wave kernel as a forcing term. We explore how the method of approximate particular solutions can be applied to obtain numerical solutions of partial differential equations such as the Poisson and heat equations with Dirichlet boundary conditions in 1D. Numerical experiments carried out in MATLAB validate that the derived closed-form particular solutions provide accurate numerical results, demonstrating the effectiveness of the proposed approach.
Recommended Citation
Smith, Braylon and Lamichhane, Anup
(2026)
"Numerical Solutions of the Poisson and Heat Equations via Wave Kernel-Based Particular Solutions,"
Electronic Proceedings of Undergraduate Mathematics Day: Vol. 9, Article 1.
Available at:
https://ecommons.udayton.edu/epumd/vol9/iss1/1