Stability of Splitting Methods For Systems of
Nonlinear Ordinary Differential Equations

Lin Lin Hteik

doi:https://doi.org/10.14445/22315373/IJMTT-V67I1P506

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 67 | Issue 1 | Year 2021 | Article Id. IJMTT-V67I1P506 | DOI : https://doi.org/10.14445/22315373/IJMTT-V67I1P506

Stability of Splitting Methods For Systems of Nonlinear Ordinary Differential Equations

Lin Lin Hteik

Citation :

Lin Lin Hteik, "Stability of Splitting Methods For Systems of Nonlinear Ordinary Differential Equations," International Journal of Mathematics Trends and Technology (IJMTT), vol. 67, no. 1, pp. 36-43, 2021. Crossref, https://doi.org/10.14445/22315373/IJMTT-V67I1P506

Abstract

In this paper, we present some numerical methods for the approximate solution of system of nonlinear ordinary differential equations. We discuss alternating direction implicit methods and approximate matrix factorization methods, both of which are splitting methods. Stability of methods is also investigated.

Keywords

The Peaceman-Rachford method, the Douglas method and Approximate Matrix Factorization (AMF) methods

References

[1] J. Frank, W.H. Hundsdorfer and J.G. Verwer, Stability of Implicit-Explicit Linear Multistep Methods, Research Report NM-R9623, ISSN 0169-0388, (1996), Amsterdam, Netherlands.
[2] W. Hundsdorfer, and J.G Verwer, Numerical Solution of Time-Dependent Advection-Diffusion-Reaction Equations, (2003), Springer-Verlag, Berlin.
[3] J.W. Thomas, Numerical Partial Differential Equations: Conservation Laws and Elliptic Equations, (1999), Springer-Verlag Inc., New York.