Identifying the temperature distribution in a parabolice quation with overspecified data using a multiquadric quasi-interpolation method

In this paper, we use a kind of univariate multiquadric quasi-interpolation to solve a parabolic equation with overspecified data, which has arisen in many physical phenomena. We obtain the numerical scheme by using the derivative of the quasi-interpolation to approximate the spatial derivative of the dependent variable and a simple forward difference to approximate the temporal derivative of the dependent variable. The advantage of the presented scheme is that the algorithm is very simple so it is very easy to implement. The results of the numerical experiment are presented and are compared with the exact solution to confirm the good accuracy of the presented scheme.