In this study, the multistep method is applied to the STF system.
This method has been tested on the STF system, which is a three-dimensional
system of ODE with quadratic nonlinearities. A computer based Matlab program
has been developed in order to solve the STF system. Stable and unstable
position of the system has been analyzed graphically and finally a comparison
as well as accuracy between two-step sizes with detail. Newton’s method has
been applied to show the best convergence of this system.
Cite this paper
S. Khan, Y. Shu and S. Khan, "Stability Control of Stretch-Twist-Fold Flow by Using Numerical Methods," World Journal of Mechanics, Vol. 2 No. 6, 2012, pp. 334-338. doi: 10.4236/wjm.2012.26039.
 C. Baker and E. Buckwar, “Numerical Analysis of Explicit One-Step Methods for Stochastic Delay Differential Equations,” LMS Journal of Computation and Mathematics, Vol. 3, No. 3, 2000, pp. 315-335.
 R. H. Bokor, “On Two-Step Methods for Stochastic Differential Equations,” Acta Cybernetica, Vol. 13, No. 1, 1997, pp. 197-207.
 L. Brug-nano, K. Burrage and P. Burrage, “Adams-Type Methods for the Numerical Solution of Stochastic Ordinary Differential Equations,” BIT Numerical Mathematics, Vol. 40, No. 3, 2000, pp. 451-470.
 E. Buckwar and R. Winkler, “On Two-Step Schemes for SDEs with Small Noise,” Proceedings in Applied Mathematics and Mechanics, Vol. 4, No. 1, 2004, pp. 15-18.
 H. B. Keller, “Approxima-tion Method for Nonlinear Problem with Application to Two Point Value Boundary Problem,” Mathematics of Computation, Vol. 29, No. 130, 1975, pp. 464-474.
 C. Lubich, “On the Convergence of Multistep Methods for Nonlinear Stiff Diffe-rential Equations,” Numerische Mathematik, Vol. 61, No. 1, 1992, pp. 277-279.
 J. O. Fatokun and I. K. O. Aji-bola, “A Collocation Multistep Method for Integrating Ordinary Differential Equations on Manifolds,” African Journal of Mathematics and Computer Science Research, Vol. 2, No. 4, 2009, pp. 51-55.