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.
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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
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
Ford N J, Lumb P M. Mixed-type functional differential equations: a numerical approach. J Comput Appl Math (available electronically)
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
Iakovleva V, Vanegas C. On the solution of differential equations with delayed and advanced arguments. Electronic Journal of Differential Equations, Conference 13, 2005, 57–63
Mallet-Paret J. The Fredholm alternative for functional differential equations of mixed type. Journal of Dynamics and Differential Equations, 1999, 11(1): 1–47
Mallet-Paret J, Verduyn Lunel S M. Mixed-type functional differential equations, holomorphic factorization and applications. In: Proceedings of Equadiff 2003, International Conference on Differential Equations, HASSELT 2003. Singapore: World Scientific, 2005, 73–89
Prenter P M. Splines and Variational Methods. New York: J Wiley and Sons, 1975, 298
Rustichini A. Functional differential equations of mixed type: the linear autonomous case. Journal of Dynamics and Differential Equations, 1989, 1(2): 121–143
Rustichini A. Hopf bifurcation of functional differential equations of mixed type. Journal of Dynamics and Differential Equations, 1989, 1(2): 145–177
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Teodoro, F., Lima, P.M., Ford, N.J. et al. New approach to the numerical solution of forward-backward equations. Front. Math. China 4, 155–168 (2009). https://doi.org/10.1007/s11464-009-0006-8
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DOI: https://doi.org/10.1007/s11464-009-0006-8