Solving Fourth Order Differential Equations Using Particular Solutions of Helmholtz-Type Equations
Mathematics and Natural Sciences
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.
Applied Mathematics Letters
(2018). Solving Fourth Order Differential Equations Using Particular Solutions of Helmholtz-Type Equations. Applied Mathematics Letters, 86, 179-185.
Available at: https://aquila.usm.edu/fac_pubs/16965