Application of statistical spline model for solving inverse source parabolic problems
Inverse parabolic problems are the most famous ill-posed problems. Thus using stable inexact numerical methods for approximating these problems, causes a large perturbation. In this paper, we study the problem of determining the source term of the inverse source problem [{partial _t}T(x,t) = kappa ,{nabla ^2}T(x,t) + g(t)delta (x - {x^*}),x in {( circ ,,1)^d},t in ( circ ,,{t_f}),] from the measured data given in the form of [T({x_{measure}},{t_i}) = {y_i}, ,i = 1,2, ldots ,I,] (additional condition) where d = 1,2 and [delta ] is the Dirac delta function and (T,g) are the unknown functions. Then, using the statistical spline model and applying Levenberg-Marquardt method, we obtain an approximate solution for quasi solution g=g(t). Finally, to show the priority and accuracy of the introduced method some numerical examples are given
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