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Applications of Higher Order Partial Differential Equations: An Analytical Solution
PINKEY
Abstract:
Separation of variables has long been acknowledged as one of the most effective methods for resolving linear partial differential equations (PDEs). In this research, an analytical solution to higher order homogeneous partial differential equations (PDEs) within a rectangular domain with specified boundary conditions (BCs) is proposed. Initially, the partial differential equation (PDE) is reduced to an ordinary differential equation (ODE) by means of variable separation and integral components. The analytical answer is obtained by using a power series expansion of the unknown function after symbolic manipulations. This paper presents a special instance of variable separation, where the PDE on one variable is solved by removing the other variable.