| Abstract: | The alternating-direction collocation (ADC) method can be formulated for general parabolic partial differential equations. This is done using a piecewise cubic Hermite trial space defined on a rectangular discretization. As in all alternating-direction methods, the ADC algorithm produces errors that are additional to the standard discretization errors of multi-dimensional collocation. These errors increase when the coefficients of the governing equation are spatially variable. Analysis of the additional errors leads to several correction schemes. Numerical results indicate that a variant on the Laplace-modification procedure is an attractive choice as an improved ADC algorithm. |
