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He’s homotopy perturbation method for nonlinear differential-difference equations. (English) Zbl 1192.65102
Summary: A new scheme, deduced from {\it J. He}’s [Comput. Methods Appl. Mech. Eng. 178, No. 3--4, 257--262 (1999; Zbl 0956.70017)] homotopy perturbation method (HPM), is presented for solving nonlinear differential-difference equations (DDEs). A simple but typical example is applied to illustrate the validity and great potential of the generalized HPM in solving nonlinear DDE. The results reveal that the method is very effective and simple.

65L05Initial value problems for ODE (numerical methods)
65L03Functional-differential equations (numerical methods)
34K28Numerical approximation of solutions of functional-differential equations
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