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

机译：积分微分方程的数值解法和改进Legendre方法的种群模型的应用

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摘要

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.
机译：本文针对一类涉及种群模型的积分-微分方程，提出了一种改进的勒让德搭配方法。通过使用算子方程的残差函数可以实现这一改进。由残差函数获得的误差微分方程已通过勒让德搭配算法（LCM）求解。通过将误差微分方程的近似解与问题的近似解相加，可以获得更好的近似解。我们给出了说明性的例子来证明该方法的有效性。我们还将我们的结果与已知某些方法的结果进行比较。另外，应用了人口模型。

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