A local meshless method for the numerical solution of space-dependent inverse heat problems

In this paper, a local radial basis function collocation method is proposed for the numerical solution of inverse space-wise dependent heat source problems. Multiquadric radial basis function is used for spatial discretization. The method accuracy is tested in terms of absolute root mean square and relative root mean square error norms. Numerical tests on a noisy data are performed on both regular domain and irregular domain. To test the efficiency and accuracy of the proposed method, numerical experiments for one-, two-, and three-dimensional cases are performed. Both regular and irregular geometries with uniform and nonuniform points are taken into consideration, and the numerical results are also compared with the existing methods reported in literature.