Solving fourth order differential equations using particular solutions of Helmholtz-type equations
The main focus of this article is the numerical solution of a fourth-order partial differential equation of the form $\left(\Delta^2-\lambda^2\right) u=f$ in a closed and bounded domain $\Omega$ with appropriate boundary conditions using the method of particular solutions. However, the derivation of a closed form particular solution is far from being trivial. Therefore, the authors provide a simple algebraic procedure to avoid this derivation. A numerical example complements their proposed approach.
scientific article; zbMATH DE number 7025994