ABSTRACT In this paper, a new method is used based on polynomials equipped with a parameter to solve two parabolic inverse problems. These inverse problems have nonlocal boundary conditions and over-determination of data that make it difficult to solve these problems. In this method, we use the combination of the finite difference method and the finite element method. In each point , a nonlinear equation system is solved via the least-squares method, and then, we obtain an approximate function for the solution of the problem by using the interpolation of these points.

中文翻译：

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一种基于带参数多项式求解具有非局部边界条件的两个抛物线反问题的新方法

摘要 在本文中，一种基于带参数多项式的新方法用于求解两个抛物线逆问题。这些逆问题具有非局部边界条件和数据的超定性，使得这些问题难以解决。在该方法中，我们结合使用有限差分法和有限元法。在每个点 ，通过最小二乘法求解一个非线性方程组，然后利用这些点的插值得到求解问题的近似函数。