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Approximate solution for system of differential-difference equations by means of the homotopy analysis method. (English) Zbl 1221.65159

The author applies the homotopy analysis method (HAM) to the solution of a system of differential-difference equations and to a Toda lattice system. The paper provides background information on HAM, shows how the method can be generalised to differential-difference equations and Toda lattice systems and finally considers some convergence results on the performance of the method. The conclusion drawn in the paper is that if the series solution converges, then it converges to an exact solution.

MSC:

65L03 Numerical methods for functional-differential equations
65L20 Stability and convergence of numerical methods for ordinary differential equations
34A25 Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc.
34K28 Numerical approximation of solutions of functional-differential equations (MSC2010)
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