A New Collocation Method for Backward and Boundary Inverse Heat Conduction Problems

In this study a modified numerical scheme using meshless procedure is proposed to solve the inverse heat conduction boundary value problems. Homotopy perturbation method (HPM) is adopted for trial functions of the collocation method used. The resultant functions are used as basis functions and an ill-conditioned system of equations is obtained by a simple collocation. To regularize the resultant ill-conditioned system of linear equations, the Tikhonov regularization technique and the L-curve were applied. Note, the approach is readily extendable to solve inhomogenous problems. The results indicate that the approach used provides a relatively accurate scheme.