Discrete models for the cube-root differential equation

Neural, Parallel and Scientific Computations

Volumn 16, Issue 2, 2008, Pages 179-188

  Ehrhardt, Matthias ^a   Mickens, Ronald E ^b  

^a TECHNISCHE UNIVERSITÄT BERLIN   (Germany)

^b CLARK ATLANTA UNIVERSITY   (United States)

Author keywords

Nonlinear oscillations; Nonstandard finite differences; Periodic solutions; Stability of numerical solutions

Indexed keywords

EID: 49549122033     PISSN: 10615369     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (19)

1. 1/3 potential, J. Sound and Vibration 246 (2001), 375-378.
2. 1/3 force oscillators, J. Sound and Vibration 292 (2006), 964-968.
3. R.E. Mickens, Exact solutions to a finite-difference model of a nonlinear reaction-advection equation: Implications for numerical analysis, Num. Meth. Partial Differential Eqs. 5 (1989), 313-325.
4. R.E. Mickens, Nonstandard Finite Difference Models of Differential Equations, World Scientific, Singapore, 1994.
5. R.E. Mickens, editor, Applications of Nonstandard Finite Difference Schemes, World Scientific, Singapore, 2000.
6. S.L. Ross, Differential Equations, Blaisdell, London, 1964.
7. R.E. Mickens, Mathematical Methods for the Natural and Engineering Sciences, World Scientific, Singapore, 2004.
8. I.S. Gradshteyn and I.M. Ryzhik, Tables of Integrals, Series and Products, Academic Press, New York, 1980.
9. F.B. Hildebrand, Finite-Difference Equations and Simulations, Prentice-Hall, Englewood Cliffs, NJ, 1968.
10. J.D. Lambert, Numerical Methods for Ordinary Differential Systems, Wiley, New York, 1991.
11. R.E. Mickens, Construction of finite dfference schemes for coupled nonlinear oscillators derived from a discrete energy function, J. Diff. Eqs. Appl. 2 (1996), 185-193.
12. R. Anguelov and J.M.-S. Lubuma, Contributions to the mathematics of the nonstandard finite difference method and applications, Num. Meth. Partial Differential Eqs. 17 (2001), 518-543.
13. X. Wang, E.K. Blum and Q. Li, Local dynamics and bifurcation consistencies of continuous - time dynamical systems and their numerical discretizations, Proceedings of Symposia in Applied Mathematics 48 (1994), 399-402.
14. R.E. Mickens, Analytical and numerical study of a non-standard finite difference scheme for the unplugged van der Pol equation, J. Sound and Vibration 245 (2001), 757-761.
15. J.M. Sanz-Serna, An unconventional symplectic integrator of W. Kahan, Appl. Numer. Math. 16 (1994), 245-250.
16. R.E. Mickens, A nonstandard finite difference scheme for the Lotka-Volterra system, Appl. Numer. Math. 45 (2003), 309-314.
17. L.-I.W. Roeger, Nonstandard finite difference schemes for the Lotka-Volterra systems: Generalization of Mickens' method, J. Diff. Eqs. Appl. 12 (2006), 937-948.
18. J.R. Dormand and P.J. Prince, A family of embedded Runge-Kutta formulae, J. Comp. Appl. Math. 6 (1980), 19-26.
19. R.E. Mickens, Dynamic consistency: A fundamental principle for constructing nonstandard finite differences for differential equations, J. Diff. Eqs. Appl. 11 (2005), 645-653.