Numerical solution of some iterative differential equation. (English) Zbl 0961.65066

The author studies the numerical solution of a state-dependent iterative differential equation. He discusses some simple algorithms based on linear and quadratic splines for the numerical solution and exhibits some computational results for various values of the parameters involved.


65L05 Numerical methods for initial value problems involving ordinary differential equations
34K28 Numerical approximation of solutions of functional-differential equations (MSC2010)


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[1] Blaga P., Kobza J., Micula G.: Low order splines in solving neutral delay differential equations. Studia Univ. Babes-Bolyai, Math. 41, (2) 1996, 73-85. · Zbl 1009.65044
[2] Hale J. K., Verduyn Lunel S. M.: Introduction to Functional Differential Equations. Springer Verlag, New York 1993. · Zbl 0787.34002
[3] Elsgolc L. E., Norkin S. B.: Introduction to Theory of Delay Differential Equations. Moscow 1971)
[4] Kobza J.: Solution of functional equation x(x(t)) = f(t). Preprint Dept. MAAM, FS UP Olomouc, 1997. · Zbl 0945.65143
[5] Kuczma M., Choczewski B., Ger R.: Iterative Functional Equations. Cambridge Univ. Press, 1990. · Zbl 0703.39005
[6] Stan\?k S.: Global properties of increasing solutions for the equation x’(t) = x(x(t)) - bx(t). Preprint Dept. MAAM, FS UP Olomouc, 1997. · Zbl 0901.34064
[7] Staněk S.: On global properties of solutions of functional diff. equation x’(t) = x(x(t)) + x(t). Dynamic Systems and Applications 4, (1995), 263-278. · Zbl 0830.34064
[8] Staněk S.: Global properties of decreasing solutions of the equation x’(t) = x(x(t))+x(t). Functional Differential Equations, V.4 (1997), 1-2. · Zbl 0901.34064
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