New approach to the numerical solution of forward-backward equations

Filomena Teodoro, Pedro M. Lima, Neville J. Ford, Patricia M. Lumb

Front. Math. China ›› 2009, Vol. 4 ›› Issue (1) : 155-168.

PDF(334 KB)
Front. Math. China All Journals
PDF(334 KB)
Front. Math. China ›› 2009, Vol. 4 ›› Issue (1) : 155-168. DOI: 10.1007/s11464-009-0006-8
Research Article
RESEARCH ARTICLE

New approach to the numerical solution of forward-backward equations

Author information +
History +

Abstract

This paper is concerned with the approximate solution of functional differential equations having the form: x′(t) = αx(t) + βx(t - 1) + γx(t + 1). We search for a solution x, defined for t ∈ [−1, k], k ∈ ℕ, which takes given values on intervals [−1, 0] and (k-1, k]. We introduce and analyse some new computational methods for the solution of this problem. Numerical results are presented and compared with the results obtained by other methods.

Keywords

Mixed-type functional differential equations / collocation method / theta-method / method of steps

Cite this article

Download citation ▾
Filomena Teodoro, Pedro M. Lima, Neville J. Ford, Patricia M. Lumb. New approach to the numerical solution of forward-backward equations. Front. Math. China, 2009, 4(1): 155‒168 https://doi.org/10.1007/s11464-009-0006-8
This is a preview of subscription content, contact us for subscripton.

References

[1.]
Abell K. A., Elmer C. E., Humphries A. R., Vleck E. S. Computation of mixed type functional differential boundary value problems. SIAM Journal on Applied Dynamical System, 2005, 4(3): 755-781.
CrossRef Google scholar
[2.]
Chi H., Bell J., Hassard B. Numerical solution of a nonlinear advance-delay-differential equation from nerve conduction theory. J Math Biol, 1986, 24: 583-601.
CrossRef Google scholar
[3.]
Ford N J, Lumb P M. Mixed-type functional differential equations: a numerical approach. J Comput Appl Math (available electronically)
[4.]
Ford N J, Lumb P M. Mixed-type functional differential equations: a numerical approach (extended version). Technical Report, 2007: 3. Department of Math, University of Chester. 2007
[5.]
Iakovleva V, Vanegas C On the solution of differential equations with delayed and advanced arguments. Electronic Journal of Differential Equations, Conference, 2005, 13: 57-63.
[6.]
Mallet-Paret J. The Fredholm alternative for functional differential equations of mixed type. Journal of Dynamics and Differential Equations, 1999, 11(1): 1-47.
CrossRef Google scholar
[7.]
Mallet-Paret J., Verduyn Lunel S. M. Mixed-type functional differential equations, holomorphic factorization and applications, 2005, Singapore: World Scientific, 73-89.
[8.]
Prenter P. M. Splines and Variational Methods, 1975, New York: J Wiley and Sons, 298
[9.]
Rustichini A. Functional differential equations of mixed type: the linear autonomous case. Journal of Dynamics and Differential Equations, 1989, 1(2): 121-143.
CrossRef Google scholar
[10.]
Rustichini A. Hopf bifurcation of functional differential equations of mixed type. Journal of Dynamics and Differential Equations, 1989, 1(2): 145-177.
CrossRef Google scholar
AI Summary AI Mindmap
PDF(334 KB)

714

Accesses

19

Citations

Detail

Sections
Recommended

/