... differential equation Homotopy analysis method Variational iteration method Caputo fractional derivative Series solution Differential equations Mathematics The homotopy analysis method (HAM) is developed by Liao (1992) . Based on homotopy of topology, the validity of the HAM is independent...

...)‐dimensional dispersive long wave equation (2+1)‐dimensional dispersive long wave equation Topology Solutions Mathematics In the study of equations modeling wave phenomena, one of the fundamental objects of study is traveling wave solution, meaning a solution of constant form moving with fixed...

... solutions. The authors believe that the new method is a promising technique in finding the exact solutions for a wide variety of mathematical problems. Originality/value The basic idea described in this paper is expected to be further employed to solve other functional equations. Mostafa Eslami can...

... the HPM and WHPM. Section 3 is devoted to application of WHPM on the heat transfer equation. In Section 4, we solve an illustrative numerical experiment to show the capability of the method. The discussions and conclusions of the study are presented in Section 5. Mathematics Programming...

.../R; R is the Reynolds number. Ram Jiwari can be contacted at: ram1maths@gmail.com © Emerald Group Publishing Limited 2012 Mathematics Differential equations 1D Burgers' equation Coupled Burgers' equations 2D Burgers' equation Differential quadrature method Runge‐Kutta...

... the existing variational iteration method. Mehmet Pakdemirli can be contacted at: mpak@bayar.edu.tr © Emerald Group Publishing Limited 2012 Heat transfer Mathematics Iterative methods Perturbation method Perturbation‐iteration method Variational iteration method Perturbation...

...,β,γ≤2). The fractional derivatives are described in the Caputo sense. Design/methodology/approach By using initial values, the explicit solutions of the equation are solved with powerful mathematical tools such as He's homotopy perturbation method (HPM). Findings This result reveals...

... Dehghan can be contacted at: mdehghan@aut.ac.ir © Emerald Group Publishing Limited 2012 Heat Mathematics Differential equations One‐dimensional parabolic equation Non‐classic boundary conditions Boundary value problem Bernstein polynomial basis Ritz‐Galerkin method Consider...

... Equation 6 Equation 7 Equation 8 Equation 9 Sefa Anıl Sezer can be contacted at: sefaanilsezer.ege@gmail.com © Emerald Group Publishing Limited 2011 Differential equations Mathematics In recent years, considerable interest in fractional...

... numerical methods suitable for thermal modelling, to date only the finite difference method[ 1 , 2 ] has been used to approximate the mathematical model of heat flow in these materials used in offshore components. However, because of widespread acceptance of the finite element method and its versatility...