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- W2078551425 abstract "A general linear boundary value problem for a nonlinear system of delay differential equations (DDE in short) is reduced to a fixed-point problem v = A v with a properly chosen (generally nonlinear) operator A . The unknown fixed-point v is approximated by piecewise linear function v h defined by its values v i = v h ( t i ) at grid points t i , i = 0 , 1 , … , N , where N is a given positive integer and h = max 1 ≤ i ≤ N ( t i − t i − 1 ) . Under suitable assumptions, the existence of a fixed-point of A is equivalent to existence of so called ε ( h ) -approximate fixed-points of v h = A v h , which can be found by minimization of L 2 ( n ) norm of residuum v h − A v h with respect to the variables v i . These ε ( h ) -approximate fixed-points are used for obtaining approximate solutions of the original boundary value problem for a system of DDE. Numerical experiments with the boundary value problem for a system of delay differential equations of population dynamics as well as with two periodic boundary value problems: one for the periodic distributed delay Lotka–Volterra competition system and the second one modeling two coupled identical neurons with time-delayed connections show an efficiency of this kind of approach." @default.
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- W2078551425 date "2011-10-01" @default.
- W2078551425 modified "2023-09-30" @default.
- W2078551425 title "Solving boundary value problems for delay differential equations by a fixed-point method" @default.
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- W2078551425 doi "https://doi.org/10.1016/j.cam.2011.09.021" @default.
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