Multiple Timewise Coefficient Determination Problem From Heat Moment Observations

Abstract

Consider the inverse problem of determining multiple timewise coeffcient and the solution function satisfying the parabolic equation with the direct initial and Dirichlet boundary conditions from the heat moment observations. This formulation ensures the unique solvability of the inverse problem. However, the problem still suffers from ill-posedness. Since small errors in the input data cause large errors in the output solution. The finite difference method is developed as a direct solver, whilst the inverse problem solver is reformulated as nonlinear least-squares minimization. The optimization problem was solved numerically using the lsqnonlin routine from the MATLAB toolbox. The exact and noisy input data are inverted numerically. Numerical results are presented and discussed to illustrate the performance of the inversion for timewise coefficients.