Premium
Generalized alternating‐direction collocation methods for parabolic equations. I. Spatially varying coefficients
Author(s) -
Celia Michael A.,
Pinder George F.
Publication year - 1990
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.1690060302
Subject(s) - mathematics , piecewise , discretization , collocation (remote sensing) , mathematical analysis , collocation method , hermite polynomials , alternating direction implicit method , parabolic partial differential equation , partial differential equation , orthogonal collocation , laplace transform , variable (mathematics) , differential equation , finite difference method , ordinary differential equation , remote sensing , geology
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.