Numerical solutions of integro-differential equations and application of a population model with an improved Legendre method.

*(English)*Zbl 1349.65728Summary: In this paper, an improved Legendre collocation method is presented for a class of integro-differential equations which involves a population model. This improvement is made by using the residual function of the operator equation. The error differential equation, gained by residual function, has been solved by the Legendre collocation method (LCM). By summing the approximate solution of the error differential equation with the approximate solution of the problem, a better approximate solution is obtained. We give the illustrative examples to demonstrate the efficiency of the method. Also we compare our results with the results of the known some methods. In addition, an application of the population model is made.

##### MSC:

65R20 | Numerical methods for integral equations |

65L60 | Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations |

45J05 | Integro-ordinary differential equations |

34K28 | Numerical approximation of solutions of functional-differential equations (MSC2010) |

92D25 | Population dynamics (general) |