Use of Smoothing Techniques in the Method of Lines

摘要

A space discretization method for parabolic partial differential equations which is based on conventional discretization techniques and smoothing matrices is described. The method leads to systems of ordinary differential equations (ODE) which are considerably less stiff than the ODEs obtained by conventional discretization methods. It turns out that the stiffness is reduced to an extent that ordinary predictor-corrector methods become feasible integration methods. Experiments illustrate this type of space discretization method.