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A higher-order compact ADI method with monotone iterative procedure for systems of reaction–diffusion equations
- Source :
- Computers & Mathematics with Applications. 62(6):2434-2451
- Publication Year :
- 2011
- Publisher :
- Elsevier BV, 2011.
-
Abstract
- This paper is concerned with an existing compact finite difference ADI method, published in the paper by Liao et al. (2002) [3], for solving systems of two-dimensional reaction–diffusion equations with nonlinear reaction terms. This method has an accuracy of fourth-order in space and second-order in time. The existence and uniqueness of its solution are investigated by the method of upper and lower solutions, without any monotone requirement on the nonlinear reaction terms. The convergence of the finite difference solution to the continuous solution is proved. An efficient monotone iterative algorithm is presented for solving the resulting discrete system, and some techniques for the construction of upper and lower solutions are discussed. An application using a model problem gives numerical results that demonstrate the high efficiency and advantages of the method.
- Subjects :
- Iterative method
System of reaction–diffusion equations
Mathematical analysis
Finite difference
Compact finite difference
Discrete system
Alternating direction implicit method
Nonlinear system
Computational Mathematics
Monotone polygon
Upper and lower solutions
Computational Theory and Mathematics
ADI method
Modeling and Simulation
Modelling and Simulation
Uniqueness
Higher-order accuracy
Monotone iterations
Mathematics
Subjects
Details
- ISSN :
- 08981221
- Volume :
- 62
- Issue :
- 6
- Database :
- OpenAIRE
- Journal :
- Computers & Mathematics with Applications
- Accession number :
- edsair.doi.dedup.....551ddd1f202efd1ad57fedec595d4078
- Full Text :
- https://doi.org/10.1016/j.camwa.2011.07.030