Solving Fourth Order Differential Equations Using Particular Solutions of Helmholtz-Type Equations

Wanru Chang, Taiyuan University
Ching-Shyang Chen, University of Southern Mississippi
Wen Li, Taiyuan University


The availability of the closed-form particular solution for a given differential equation based on a chosen basis function is crucial for solving partial differential equations using the method of particular solutions. In general, the derivation of such a closed-form particular solution is by no means trivial, particularly for higher order partial differential equations. In this paper we give a simple algebraic procedure to avoid the direct derivation of the closed-form particular solutions for fourth order partial differential equations. One numerical example is given to demonstrate the effectiveness of our proposed approach.