Use of Picard and Newton iteration for solving nonlinear ground water flow equations
Ground Water
By: S. Mehl
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Abstract
This study examines the use of Picard and Newton iteration to solve the nonlinear, saturated ground water flow equation. Here, a simple three-node problem is used to demonstrate the convergence difficulties that can arise when solving the nonlinear, saturated ground water flow equation in both homogeneous and heterogeneous systems with and without nonlinear boundary conditions. For these cases, the characteristic types of convergence patterns are examined. Viewing these convergence patterns as orbits of an attractor in a dynamical system provides further insight. It is shown that the nonlinearity that arises from nonlinear head-dependent boundary conditions can cause more convergence difficulties than the nonlinearity that arises from flow in an unconfined aquifer. Furthermore, the effects of damping on both convergence and convergence rate are investigated. It is shown that no single strategy is effective for all problems and how understanding pitfalls and merits of several methods can be helpful in overcoming convergence difficulties. Results show that Picard iterations can be a simple and effective method for the solution of nonlinear, saturated ground water flow problems.
Suggested Citation
Mehl, S., 2006, Use of Picard and Newton iteration for solving nonlinear ground water flow equations: Ground Water, v. 44, no. 4, p. 583-594, https://doi.org/10.1111/j.1745-6584.2006.00207.x.
| Publication type | Article |
|---|---|
| Publication Subtype | Journal Article |
| Title | Use of Picard and Newton iteration for solving nonlinear ground water flow equations |
| Series title | Ground Water |
| DOI | 10.1111/j.1745-6584.2006.00207.x |
| Volume | 44 |
| Issue | 4 |
| Publication Date | June 30, 2006 |
| Year Published | 2006 |
| Language | English |
| Larger Work Type | Article |
| Larger Work Subtype | Journal Article |
| Larger Work Title | Ground Water |
| First page | 583 |
| Last page | 594 |