Solving partial differential equation by using multiquadric quasi-interpolation

In this paper, we use a kind of univariate multiquadric (MQ) quasi-interpolation to solve partial differential equation (PDE). We obtain the numerical scheme, by using the derivative of the quasi-interpolation to approximate the spatial derivative of the dependent variable and a low order forward difference to approximate the temporal derivative of the dependent variable. The advantage of the resulting scheme is that the algorithm is very simple so it is very easy to implement. Our numerical experiment includes two examples. One is solving viscid Burgers’ equation for initial trapezoidal conditions. Another is simulating the interaction of two waves travelling in opposite direction. From the numerical experiment, we can see that the present scheme is valid.