The aim of this paper is to present a reproducing kernel method for solving system of integro-differential equations with nonlocal boundary conditions. The solution obtained by using the present method takes the form of a convergent series with easily computable components. The analysis of convergence shows that the approximate solution and its derivatives converge to the exact solution and its derivatives, respectively. The numerical examples are given to demonstrate the accuracy of the present method. Results obtained by using the present method are compared with those of the exact solution of each example and are found to be in good agreement.

中文翻译：

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具有非局部边界条件的积分微分方程组的求解的一种再生核方法

本文的目的是提出一种求解具有非局部边界条件的积分-微分方程组的再现核方法。通过使用本发明的方法获得的解采取具有容易计算的分量的收敛级数的形式。收敛分析表明，近似解及其导数分别收敛于精确解及其导数。数值例子说明了本方法的准确性。将使用本方法获得的结果与每个实施例的精确解决方案的结果进行比较，发现结果吻合良好。