Abstract The main target of the paper is solving a system of two-dimensional Volterra integral equations (2-DVIE) and receiving convincing solutions. We change the problem to a system of simpler equations by Legendre wavelets. By merging properties of wavelets to system and reducing the number of variables we build more powerful tools than some other methods. 3 examples and proof of convergence verify the applicability of the new numerical technique.

中文翻译：

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基于勒让德小波和收敛的二维沃尔泰拉积分方程组的数值解

摘要 本文的主要目标是求解二维沃尔泰拉积分方程组（2-DVIE）并获得令人信服的解。我们通过勒让德小波将问题转换为更简单的方程组。通过将小波的属性合并到系统中并减少变量的数量，我们构建了比其他一些方法更强大的工具。3 个例子和收敛性证明验证了新数值技术的适用性。