Knk. Kumar et V. Eswaran, A FULLY SPECTRAL SOLUTION METHOD FOR PARABOLIC EQUATIONS, Communications in numerical methods in engineering, 11(9), 1995, pp. 765-774
A comparison is made between the performance of the (aliased) Chebyshe
v collocation method (CM) and the more recent Galerkin collocation met
hod (GCM), which is a least-squares collocation method, in solving the
laminar, incompressible, steady boundary-layer equations, which are p
arabolic in nature. An iterative procedure based on the preconditioned
residual minimization method has been used. It is shown that the GCM
is superior to the CM on several counts. Unlike the CM, the GCM minimi
zes the residual uniformly over the entire domain. The global accuracy
of the solution is found to be higher in the GCM, at lower grid resol
utions. The method also achieves much higher convergence rates. Unlike
in the collocation method, the final residual values obtained in the
GCM are good indicators of the level of accuracy achieved in the solut
ion. It is highly likely that these results will be repeatable in othe
r systems of parabolic partial differential equations.