Abstract

In this paper, we introduce a new scheme based on the exponential spline function for solving linear second-order Fredholm integro-differential equations. Our approach consists of reducing the problem to a set of linear equations. We prove the convergence analysis of the method applied to the solution of integro-differential equations. The method is described and illustrated with numerical examples. The results reveal that the method is accurate and easy to apply. Moreover, results are compared with the method in (J. Comput. Appl. Math. 290:633–640, 2015).

中文翻译：

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线性Fredholm积分微分方程数值解的指数样条。

摘要

在本文中，我们介绍了一种基于指数样条函数的新方案，用于求解线性二阶Fredholm积分微分方程。我们的方法包括将问题简化为一组线性方程。我们证明了用于积分微分方程解的方法的收敛性分析。通过数值示例来描述和说明该方法。结果表明该方法准确易行。此外，结果与在方法（。：633-640，J. COMPUT应用数学290相比2015）。