A numerical solution technique for a one-dimensional inverse nonlinear parabolic problem

This study is intended to provide a new numerical algorithm for solving a one-dimensional inverse nonlinear parabolic problem. At the beginning of the study, Taylor’s series expansion is employed to linearize nonlinear terms and then finite-difference method is used to discretize the problem domain. The present approach is to rearrange the matrix forms of the differential governing equations and estimate unknown functions. The least-squares method is adopted to find the solution. It is assumed that no prior information is available on the functional form of the unknown coefficient in the present study, thus, it is classified as the function estimation. Results show that an excellent estimation on the unknown functions of the inverse problem which can be obtained within a couple of minutes CPU time at Pentium IV-2.4 GHz PC.