Journal article
Truncation error and stability analysis of iterative and non-iterative Thomas-Gladwell methods for first-order non-linear differential equations
The consistency and stability of a Thomas–Gladwell family of multistage time-stepping schemes for the solution of first-order non-linear differential equations are examined. It is shown that the consistency and stability conditions are less stringent than those derived for second-order governing equations.
Second-order accuracy is achieved by approximating the solution and its derivative at the same location within the time step. Useful flexibility is available in the evaluation of the non-linear coefficients and is exploited to develop a new non-iterative modification of the Thomas–Gladwell method that is second-order accurate and unconditionally stable.
A case study from applied hydrogeology using the non-linear Richards equation confirms the analytic convergence assessment and demonstrates the efficiency of the non-iterative formulation. Copyright © 2004 John Wiley & Sons, Ltd.
Language: | English |
---|---|
Publisher: | John Wiley & Sons, Ltd. |
Year: | 2004 |
Pages: | 2031-2043 |
ISSN: | 10970207 and 00295981 |
Types: | Journal article |
DOI: | 10.1002/nme.1035 |
ORCIDs: | Binning, Philip John |