## A numerical approximation based on the Bessel functions of first kind for solutions of Riccati type differential-difference equations.(English)Zbl 1268.65090

Summary: A collocation method based on the Bessel functions of first kind is given for the approximate solutions of the Riccati differential-difference equations under the mixed condition. The method is presented with error analysis. Numerical examples are included to demonstrate the validity and applicability of the method and the comparisons are made with existing results.

### MSC:

 65L03 Numerical methods for functional-differential equations 65L60 Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations 33C10 Bessel and Airy functions, cylinder functions, $${}_0F_1$$
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