Analysis of alternating direction collocation methods for parabolic and hyperbolic problems in two space variables

Ryan I. Fernandes, Graeme Fairweather

Research output: Contribution to journalArticlepeer-review

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Abstract

While alternating direction implicit (ADI) collocation methods have been used for several years to solve parabolic problems in several space variables, no convergence analysis has been derived for any of these methods. We formulate and rigorously analyze ADI collocation schemes applied to the inhomogeneous heat and wave equations on the unit square subject to homogeneous Dirichlet boundary conditions and appropriate initial conditions. We prove that each method is second‐order accurate in time and of optimal accuracy in space in the L2 and H01 norms. Numerical experiments confirm the predicted rates of convergence. © 1993 John Wiley & Sons, Inc.

Original languageBritish English
Pages (from-to)191-211
Number of pages21
JournalNumerical Methods for Partial Differential Equations
Volume9
Issue number2
DOIs
StatePublished - Mar 1993

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