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Numerical solutions of integro-differential equations and application of a population model with an improved Legendre method. (English) Zbl 1349.65728
Summary: 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)
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