In this paper, a new method using hyperbolic basis functions is presented to solve second kind linear Volterra‐Fredholm integral equation. In other words, our method approximates the solution of a Volterra‐Fredholm integral equation by the hyperbolic basis functions, which produce block‐pulse functions. Hence, the new method reduces the linear Volterra‐Fredholm integral equation to a system of algebraic equations. Some numerical examples are provided to illustrate the computational efficiency and accuracy of the new method.

中文翻译：

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Volterra-Fredholm积分方程通过双曲基函数的数值解

本文提出了一种利用双曲基函数求解第二类线性Volterra-Fredholm积分方程的新方法。换句话说，我们的方法通过双曲线基函数逼近了Volterra-Fredholm积分方程的解，这产生了块脉冲函数。因此，新方法将线性Volterra-Fredholm积分方程简化为一个代数方程组。提供了一些数值示例来说明新方法的计算效率和准确性。