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On the stability and convergence of a difference scheme for an one-dimensional parabolic inverse problem. (English) Zbl 1119.65089
The article is devoted to the following inverse parabolic problem: given E(t), 0tT find p(t) and u(x,t), 0<x<1, 0tT such that u/t= 2 u/x 2 +p(t)u+ϕ(x,t), 0<x<1, 0tT; u(x,0)=f(x), 0<x<1; u(0,t)=g 0 (t), u(1,t)=g 1 (t), u(x * ,t)=E(t), 0tT. The original nonlinear problem is transformed into a linear one, and the backward Euler scheme is applied to the latter. The convergence orders of both u and p are O(τ+h 2 ).
MSC:
65M32Inverse problems (IVP of PDE, numerical methods)
65M06Finite difference methods (IVP of PDE)
65M12Stability and convergence of numerical methods (IVP of PDE)
35K55Nonlinear parabolic equations
35R30Inverse problems for PDE