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Numerical methods for solving inverse problems for time fractional diffusion equation with variable coefficient. (English) Zbl 1205.26009
The authors consider numerical methods for solving inverse problems of time fractional diffusion equation with a variable generalized diffusion coefficient. A weighted difference scheme is constructed via an integro-interpolation method and a generalized factorization method is also developed. Furthermore, results on the stability analysis of the difference schemes are presented and properties of the numerical solutions are investigated and discussed. Furthermore, the inverse problems for the time fractional diffusion equation with a variable coefficient are also formulated as residual function minimization problems and properties of the corresponding residual functions are discussed. Numerical examples are presented and well illustrated.
26A33Fractional derivatives and integrals (real functions)
65M12Stability and convergence of numerical methods (IVP of PDE)
65M32Inverse problems (IVP of PDE, numerical methods)