Stability of Splitting Methods For Systems of Nonlinear Ordinary Differential Equations

  IJMTT-book-cover
 
International Journal of Mathematics Trends and Technology (IJMTT)
 
© 2021 by IJMTT Journal
Volume-67 Issue-1
Year of Publication : 2021
Authors : Lin Lin Hteik
  10.14445/22315373/IJMTT-V67I1P506

MLA

MLA Style: Lin Lin Hteik  "Stability of Splitting Methods For Systems of Nonlinear Ordinary Differential Equations" International Journal of Mathematics Trends and Technology 67.1 (2021):36-43. 

APA Style: Lin Lin Hteik(2021). Stability of Splitting Methods For Systems of Nonlinear Ordinary Differential Equations  International Journal of Mathematics Trends and Technology, 36-43.

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.

Reference

[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.

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