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

Yüzbaşı, Şuayip; Sezer, Mehmet; Kemancı, Bayram

Appl. Math. Modelling 37, No. 4, 2086-2101 (2013).

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)

Keywords:

population model; integro-differential equations; improved Legendre collocation method; Legendre polynomials; numerical solutions