SOLUTION OF PARABOLIC PARTIAL DIFFERENTIAL EQUATIONS BY A DOUBLE COLLOCATION METHOD

A method for solution of parabolic PDE by means of interpolation of the differential operators in two dimensions is described. The method is developed on the basis of previously published methods for solution of ordinary differential equations by orthogonal collocation. It is shown to be highly economical and very stable in comparison with the conventional Crank-Nicolson or with explicit methods such as the Runge-Kutta 4th order method. The linear heat equation is used to illustrate the principle of the method and to discuss its convergence properties. © 1969.