A reliable algorithm for solving discontinued problems arising in nanotechnology

In this paper, a reliable algorithm based on new homotopy perturbation transform method (HPTM) 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 HPTM is a combined form of Laplace transform, homotopy perturbation method and Heʹs polynomials. The technique finds the solution without any discretization or restrictive assumptions and avoids the round-off errors. The numerical solutions show that the proposed method is very efficient and computationally attractive. It provides more realistic series solutions that converge very rapidly for nonlinear real physical problems.