Nonlinear Analysis 71 (2009) e630–e640 Contents lists available at ScienceDirect Nonlinear Analysis journal homepage: www.elsevier.com/locate/na Modified variational iteration technique for solving singular fourth-order parabolic partial differential equations Muhammad Aslam Noor, Khalida Inayat Noor, Syed Tauseef Mohyud-Din * Department of Mathematics, COMSATS Institute of Information Technology, Islamabad, Pakistan article info Keywords: Modified variational iteration method Homotopy perturbation method Singular fourth-order parabolic PDES Boundary value problems abstract In this paper, we apply the modified He’s variational iteration method for solving singular fourth-order parabolic partial differential equations. The proposed modification is made by introducing the He’s polynomials in the correct functional. The developed algorithm is quite efficient and is well suited practically for use in these problems. The proposed iterative scheme finds the solution without any discritization, linearization or restrictive assumptions. Several examples are given to verify the reliability and efficiency of the suggested method. The fact that the modified variational iteration method (MVIM) solves nonlinear problems without using the Adomian’s polynomials can be considered as a clear advantage of this technique over the decomposition method. © 2008 Elsevier Ltd. All rights reserved. 1. Introduction This paper is devoted to the study of the singular fourth-order parabolic partial differential equation with variable coefficient. It is well known in the literature that a wide class of problems arising in mathematics, physics, astrophysics and engineering sciences can be distinctively formulated as singular initial and boundary value problems. Singular fourth- order parabolic partial differential equations govern the transverse vibrations of a homogeneous beam. Such types of equation arise in the mathematical modeling of viscoelastic and inelastic flows, deformation of beams and plate deflection theory, see [1–7,41,42]. The studies of such problems have attracted the attention of many mathematicians and physicists. For simplicity, consider the singular fourth-order parabolic partial differential equation with a variable co-efficient of the form: ∂ 2 u ∂ t 2 + μ(x, y, z ) ∂ 4 u ∂ x 4 + 1 y λ(x, y, z ) ∂ 4 u ∂ y 4 + 1 z η(x, y, z ) ∂ 4 u ∂ z 4 = g (x, y, z , t ), z < y, y, z < b, t > 0 (where μ(x, y, z ), λ(x, y, z ), and η(x, y, z ) are positive) subject to the initial conditions u(x, y, z , t ) = g 0 (x, y, z ), ∂ u ∂ t (x, y, z , 0) = f 0 (x, y, z ), and the boundary conditions * Corresponding author. Tel.: +92 3335151290; fax: +92 512831310. E-mail addresses: noormaslam@hotmail.com (M.A. Noor), khalidanoor@hotmail.com (K.I. Noor), syedtauseefs@hotmail.com (S.T. Mohyud-Din). 0362-546X/$ – see front matter © 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.na.2008.11.011