Numerical method of solving inverse problem to diffusion equation with nonlocal boundary condition
Keywords:
inverse problem, heat equation, nonlocal boundary conditions, spectral method, minimizing of the residual functional, collocation methodAbstract
The nonlocal boundary value problems for parabolic equations are actively studied and have great practical interests, because such equations describe applied problems of mechanics, physics and biology. In this paper we consider one-dimensional inverse problem of identifying the source function for the heat equation by the final temperature measurements with nonlocal boundary conditions. The problem is solved by the method of regularization of the residual functional. The method of collocation is developed and numerically implemented. The developed method allowed to implement a large number of numerical examples and were calculated for different sets of parameters such as the number of terms in the expansion K, the regularization parameter μ, the parameter α in the boundary conditions, observation time T. We also investigated the variants with different character of unknown source function f(x) and reconstructed it with accuracy close to the computer. Fast oscillating and discontinuous functions also reconstructed with satisfactory accuracy.
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