In this work, an efficient algorithm is proposed for solving the system of Volterra integral equations based on wavelet Galerkin method. This problem is reduced to a set of algebraic equations using the operational matrix of integration and wavelet transform matrix. For linear type, the computational effort decreases by thresholding. The convergence analysis of the proposed scheme has been investigated and it is shown that its convergence is of order $O\left(2^{-Jr}\right)$, where J is the refinement level and r is the multiplicity of multi-wavelets. Several numerical tests are provided to illustrate the ability and efficiency of the method.

中文翻译：

---

Volterra积分方程组的多小波Galerkin方法。

在这项工作中，提出了一种基于小波Galerkin方法求解Volterra积分方程组的有效算法。使用积分运算矩阵和小波变换矩阵，将该问题简化为一组代数方程。对于线性类型，计算量通过阈值减少。研究了该方案的收敛性分析，表明其收敛性是有序的$Ø（2^{-Ĵ\mathrm{[R}}）$，其中J是细化级别，r是多重小波的多重性。提供了一些数值测试来说明该方法的能力和效率。