AN ANALYTICAL SOLUTION FOR PARTIAL DIFFERENTAL EQUATION GOVERNING VIBRATIONS OF A RECTANGULAR MEMBRANE
One of the powerful analytical methods to solve partial differential equation is the Adomian Decomposition Method (ADM). In this paper, a general approach based on the generalized Fourier series expansion is applied to obtain an analytical solution. The solution is simplified in terms of a given orthogonal basis functions that these functions satisfy the boundary conditions. Based on the success of Fourier analysis and Hilbert space theory, orthogonal expansions undoubtedly count as fundamental concept of mathematical analysis. For the first time, We solved this equation using ADM and the results are compared with classical methods to demonstrate the accuracy of the scheme.
Adomian Decomposition Method; Fourier series expansions;Orthogonal basis functions expansions; Boundary value problems;