A radial basis function collocation method for space-dependent inverse heat problems

In this study, a radial basis function collocation method (RBFCM) is proposed for the numerical treatment of inverse space-wise dependent heat source problems. Multiquadric radial basis function is applied for spatial discretization whereas for temporal discretization Runge-Kutta method of order four is employed. Numerical experiments for one, two and three dimensional cases are included to test the efficiency and accuracy of the suggested method. Both non-rectangular and rectangular geometries with uniform and non-uniform points are taken into consideration and the obtained results are compared with the exact as well as with the techniques presented in recent literature.