Numerical Solution of Linear and Non-Linear Parabolic Differential Equations by a Time-Discretisation of Third Order Accuracy

Summary

Solving parabolic differential equations by the well-known explicit one-step method the stability condition imposes a rigorous restriction on the time step. But this condition is only a sufficient one if one considers more than one time step, say n. A slight modification of this method dramatically enlarges the time steps. In this paper a n-step method is presented which is n times faster than the known explicit one. Subsequently an extension yields a method of third order accuracy which seems to be an useful explicit alternative to the implicit Crank-Nicolson method of second order accuracy.