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

In this paperý, ýa numerical procedure for an inverse problem ofý ýsimultaneously determining an unknown coefficient in a semilinear ýparabolic equation subject to the specification of the solution atý ýan internal point along with the usual initial boundary conditions ýis consideredý. ýThe method consists of expanding the requiredý ýapproximate solution as the elements of the inverse quadraticý ýradial basis functions (IQ-RBFs)ý. ýThe operational matrix ofý ýderivative for IQ-RBFs is introduced and the new computationalý ýtechnique is used for this purposeý. ýThe operational matrix ofý ýderivative is utilized to reduce the problem to a set of algebraicý ýequationsý. ýSome examples are given to demonstrate the validity andý ýapplicability of the new method and a comparison is made with theý ýexisting results.