On the stable difference scheme for source identification nonlocal elliptic problem

Approximation of source identification problem for elliptic equation with integral‐type nonlocal condition is discussed. The first order of accuracy difference scheme for elliptic nonlocal identification problem is studied. By using spectral resolution of a self‐adjoint operator, we establish stability inequalities for solution of constructed scheme. Subsequently, the difference scheme for approximate solution of multidimensional boundary value problem with integral‐type nonlocal and first kind boundary conditions is investigated on stability. Numerical test examples are presented.

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