For a system of partial differential equations, we consider the inverse problem of determining one of the coefficients based on additional information on one of the solution components. An iterative method is proposed for calculating the unknown coefficient based on the reduction of the inverse problem to a nonlinear operator equation. The convergence of the iterative method and the existence and uniqueness of a solution of the inverse problem are proved. Numerical results illustrating the convergence of the iterative numerical method are given.

中文翻译：

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偏微分方程组反系数问题数值解的迭代法

对于偏微分方程组，我们考虑基于解分量之一的附加信息确定系数之一的逆问题。基于将逆问题简化为非线性算子方程，提出了一种迭代计算未知系数的方法。证明了迭代法的收敛性和逆问题解的存在唯一性。给出了说明迭代数值方法收敛性的数值结果。