Analytical approximate solutions for nonplanar Burgers equations by weighted residual method

Approximate Analytical Solutions of Time Fractional Whitham-Broer-Kaup Equations by a Residual Power Series Method

In this paper, a new analytic iterative technique, called the residual power series method (RPSM), is applied to time fractional Whitham–Broer–Kaup equations. The explicit approximate traveling solutions are obtained by using this method. The efficiency and accuracy of the present method is demonstrated by two aspects. One is analyzing the approximate solutions graphically. The other is compari...

Approximate Analytical Solutions of Fuzzy Linear Fredholm Integral Equations by HAM

Local method of approximate particular solutions for two-dimensional unsteady Burgers' equations

The local method of approximate particular solutions (LMAPS) is first proposed to solve Burgers’ equations. In avoiding the ill-conditioning problem, the weight coefficients of linear combination with respect to the function values and its derivatives can be obtained by solving low-order linear systems within the local supporting domain. Then the global solutions can be obtained by reformulatin...

Approximate analytical solutions for the time-dependent Emden-Fowler-type equations by Variational Homotopy Perturbation Method

In this paper, variational homotopy perturbation method (VHPM) is used to obtain analytical solution for the time-dependent Emden-Fowler type of equations with singular behavior. The advantage of this work is twofold. Firstly, the VHPM reduces the computational work. Secondly, in comparison with existing techniques, the VHPM is an improvment with regard to its accuracy and rapid convergence. To...

Approximate Solutions of General Perturbed Kdv-burgers Equations

In this article, we present some approximate analytical solutions to the general perturbed KdV-Burgers equation with nonlinear terms of any order by applying the homotopy analysis method (HAM). While compared with the Adomain decomposition method (ADM) and the homotopy perturbation method (HPM), the HAM contains the auxiliary convergence-control parameter ~ and the control function H(x, t), whi...