Abstract
We show the use of parametrization techniques and successive approximations for the effective construction of solutions of linear boundary value problems for differential systems with multiple argument deviations. The approach is illustrated with a numerical example.
Highlights
In several applications, it is desirable to have effective tools allowing one to construct solutions of functional differential equations under various boundary conditions
The classical method of steps [1] allows one to construct the solution of the Cauchy problem by extending it from the initial interval in a stepwise manner; in this way, an ordinary differential equation is solved at every step, with every preceding part of the curve serving as a historical function for the one
This technique, together with the ODE solvers available in the mathematical software, is commonly used in the practical analysis of dynamic models based on equations with retarded argument under the initial conditions
Summary
It is desirable to have effective tools allowing one to construct solutions of functional differential equations under various boundary conditions. The classical method of steps [1] allows one to construct the solution of the Cauchy problem by extending it from the initial interval in a stepwise manner; in this way, an ordinary differential equation is solved at every step, with every preceding part of the curve serving as a historical function for the one This technique, together with the ODE solvers available in the mathematical software, is commonly used in the practical analysis of dynamic models based on equations with retarded argument under the initial conditions (e.g., in economical models [4,5,6]). For an essentially bounded function v : [ a, b] → Rn and an interval J ⊆ [ a, b], we put δ J (v) := ess sup v(t) − ess inf v(t)
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