A NUMERICAL APPROACH TO SOLVING A NONLINEAR INVERSE PARABOLIC PROBLEM USING FUNDAMENTAL SOLUTION METHOD

This study is intended to provide a numerical algorithm for solving an inverse parabolic problem of linear equation with nonlinear boundary condition. To solve this inverse problem, we use the fundamental solution method. The inverse problem has a unique solution, but this solution is unstable hence the problem is ill-posed. This instability is overcome using the Tikhonov regularization method. The effectiveness of the algorithm is illustrated by numerical example. Results show that an excellent estimation on the unknown functions of the inverse problem can be obtained within a couple of minutes CPU time at pentium IV-2.4 GHz PC.