## The homotopy perturbation method for discontinued problems arising in nanotechnology.(English)Zbl 1189.65186

Summary: Continuum hypothesis on nanoscales is invalid, and a differential-difference model is considered as an alternative approach to describing discontinued problems. This paper applies the homotopy perturbation method to a nonlinear differential-difference equation arising in nanotechnology. Comparison of the approximate solution with the exact one reveals that the method is very effective.

### MSC:

 65L99 Numerical methods for ordinary differential equations 82D80 Statistical mechanics of nanostructures and nanoparticles 35Q74 PDEs in connection with mechanics of deformable solids
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### References:

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