The use of inverse quadratic radial basis functions for the solution of an inverse heat problem

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‎In this paper‎, ‎a numerical procedure for an inverse problem of‎ ‎simultaneously determining an unknown coefficient in a semilinear ‎parabolic equation subject to the specification of the solution at‎ ‎an internal point along with the usual initial boundary conditions ‎is considered‎. ‎The method consists of expanding the required‎ ‎approximate solution as the elements of the inverse quadratic‎ ‎radial basis functions (IQ-RBFs)‎. ‎The operational matrix of‎ ‎derivative for IQ-RBFs is introduced and the new computational‎ ‎technique is used for this purpose‎. ‎The operational matrix of‎ ‎derivative is utilized to reduce the problem to a set of algebraic‎ ‎equations‎. ‎Some examples are given to demonstrate the validity and‎ ‎applicability of the new method and a comparison is made with the‎ ‎existing results.