Moving grid method without interpolations

Abstract In their method of solving a one-dimensional moving boundary problem Crank and Gupta suggest a grid system which moves with the interface. The method requires some interpolations to be carried out which they perform by using a cubic spline or an ordinary polynomial. In the present paper these interpolations are avoided by employing a Taylor's expansion in space and time dimensions. A practical diffusion problem is solved and the results are compared with those obtained from other methods.