Abstract: For many decades, separation of variable is recognized as one of the most powerful techniques for solving linear partial differential equations PDEs. The present paper proposes analytical solution for higher order homogeneous partial differential equations PDEs under specified boundary conditions BCs within a rectangular domain. Firstly, separation of variables and integral factors are used to reduce the given partial differential equation PDE to an ordinary differential equation ODE. After symbolic manipulations, a power series expansion of the unknown function is utilized to create the analytical solution. The present paper is a unique case of separation of variables which rely on eliminating one variable to solve the PDE on the other variable. The proposed closed form solution presented here reduces the effort consumed for implement the alternative numerical solutions. The effectiveness of the obtained method proves the capability to provide an analytical solution overcoming the complexity of boundary conditions and mixed derivatives in the solution of higher order linear PDE.
Keywords: Partial Differential Equation, separation of variables, shape function, Power Series.
Title: Analytical Solution of Higher Order Partial Differential Equations
Author: Ahmed M. Farag El Sheikh
International Journal of Mathematics and Physical Sciences Research
ISSN 2348-5736 (Online)
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