Solution of a semilinear parabolic equation with an unknown control function using the decomposition procedure of Adomian

Abstract

The investigation of nonclassical parabolic initial-boundary value problems, which involve an integral over the spatial domain of a function of the desired solution, is of considerable concern. In this article a parabolic partial differential equation subject to energy overspecification is studied. This problem is appeared in modeling of many physical phenomena. The Adomian decomposition method, which is an efficient method for solving various class of problems, is employed for solving this model. This method provides an analytical solution in terms of an infinite convergent power series. Some examples are reported to support the simplicity of the decomposition procedure of Adomian.

Variational iteration method for modified Camassa–Holm and Degasperis–Procesi equations

“…Many powerful methods have been presented, for instance, inverse scattering method [1], Adomian's decomposition method [2][3][4], Hirota's bilinear method [5], exp-function method [6], homotopy analysis method [7], homotopy perturbation method [4,[8][9][10][11][12][13][14][15][16][17][18], variational iteration method (VIM) [19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37] and other methods [38][39][40][41][42][43].…”

The numerical solution of the second Painlevé equation

“…Employing higher order Pade approximations produces more efficient results. The ADM is employed in [48] to solve a semilinear parabolic partial differential equation and to find an unknown source control parameter.…”

Homotopy perturbation method for numerical solutions of KdV‐Burgers' and Lax's seventh‐order KdV equations

“…Many powerful methods have been presented. For instance, Backlund transformation method [1], Darboux transformation method [2], Adomian's decomposition method [3][4][5][6][7], exp-function method [8], and variational iteration method (VIM) [9][10][11][12][13].…”