Derivation of the (Closed-Form) Particular Solution of the Poisson’s Equation in 3D Using Oscillatory Radial Basis Function
Partial differential equations (PDEs) are useful for describing a wide variety of natural phenomena, but analytical solutions of these PDEs can often be difficult to obtain. As a result, many numerical approaches have been developed. Some of these numerical approaches are based on the particular solutions. Derivation of these particular solutions are challenging. This work is about how the Laplace operator can be written in a more convenient form when it is applied to radial basis functions and then use this form to derive the (closed-form) particular solution of the Poisson’s equation in 3D with the oscillatory radial function in the forcing term.
Lamichhane, Anup R. and Manns, Steven
"Derivation of the (Closed-Form) Particular Solution of the Poisson’s Equation in 3D Using Oscillatory Radial Basis Function,"
Electronic Proceedings of Undergraduate Mathematics Day: Vol. 6, Article 2.
Available at: https://ecommons.udayton.edu/epumd/vol6/iss1/2