Comparison and coupling of polynomials for singular fourth-order parabolic PDES

In this paper, we apply two modified versions of variational iteration method (VIM) to solve singular fourth-order parabolic partial differential equations. The proposed modifications are made by introducing the He’s polynomials and Adomian’s polynomials in the correction functional of VIM. The developed algorithms are quite efficient and are practically well suited for use in these problems. The proposed iterative schemes find the solution without any discritization, linearization or restrictive assumptions. Several examples are given to verify the reliability and efficiency of the suggested algorithms. It is observed that the modified version which is based upon He’s polynomials (VIMHP) is more user friendly and is easier to implement as compare to the one (VIDM) where Adomian’s polynomials along with their complexities are applied.