Kashuri, A., Fundo, A. and Kreku, M. (2013) Mixture of a New Integral Transform and Homotopy Perturbation Method for Solving Nonlinear Partial Differential Equations. Advances in Pure Mathematics, 3, 317-323. http://dx.doi.org/10.4236/apm.2013.33045

has been cited by the following article:

• TITLE: The Mixture of New Integral Transform and Homotopy Perturbation Method for Solving Discontinued Problems Arising in Nanotechnology

  AUTHORS: Kunjan Shah, Twinkle Singh

  KEYWORDS: New Integral Transform, Homotopy Perturbation Method, He’s Polynomials, Discretized mKDV Lattice Equation, Nanotechnology

  JOURNAL NAME: Open Journal of Applied Sciences, Vol.5 No.11, November 19, 2015

  ABSTRACT: In this paper, a reliable algorithm based on mixture of new integral transform and homotopy perturbation method is proposed to solve a nonlinear differential-difference equation arising in nanotechnology. Continuum hypothesis on nanoscales is invalid, and a differential-difference model is considered as an alternative approach to describing discontinued problems. The technique finds the solution without any discretization or restrictive assumptions and avoids the round-off errors. Comparison of the approximate solution with the exact one reveals that the method is very effective. It provides more realistic series solutions that converge very rapidly for nonlinear real physical problems.