Gaussian Radial Basis Functions for the Solution of an Inverse Problem of Mixed Parabolic-Hyperbolic Type

In this paper, we consider an inverse problem of mixed parabolic-hyperbolic type. This inverse problem related to finding the unknown right-hand side of the equation of mixed parabolic-hyperbolic type in a ectangular domain. We proposed a n umerical approach to solve this problem. This method is a combination of collocation method and Gaussian radial basis functions (GA-RBFs). The operational matrix of derivative for GA-RBFs is introduced. The operational matrix of derivative is utilized to reduce the problem to a set of algebraic equations. Using this method, a rapid convergent solution is produced which tends to the exact solution of the problem. The accuracy of the method is tested in term of RMS error. Some examples is included to demonstrate the validity and applicability of the technique.