Validated integration of differential equations with state-dependent delay
KEM Church - Communications in Nonlinear Science and Numerical …, 2022 - Elsevier
Communications in Nonlinear Science and Numerical Simulation, 2022•Elsevier
We present an implicit method of steps for differential equations with state-dependent delays
and validated numerics to rigorously enclose solutions of initial-value problems. Our
approach uses a combination of contraction mapping arguments based on a Newton–
Kantorovich type theorem and piecewise polynomial interpolation. Completing multiple
steps of integration is challenging, and we resolve it by smooth interpolation of the previous
solution, resulting in an interval-valued polynomial initial condition for the subsequent step …
and validated numerics to rigorously enclose solutions of initial-value problems. Our
approach uses a combination of contraction mapping arguments based on a Newton–
Kantorovich type theorem and piecewise polynomial interpolation. Completing multiple
steps of integration is challenging, and we resolve it by smooth interpolation of the previous
solution, resulting in an interval-valued polynomial initial condition for the subsequent step …
Abstract
We present an implicit method of steps for differential equations with state-dependent delays and validated numerics to rigorously enclose solutions of initial-value problems. Our approach uses a combination of contraction mapping arguments based on a Newton–Kantorovich type theorem and piecewise polynomial interpolation. Completing multiple steps of integration is challenging, and we resolve it by smooth interpolation of the previous solution, resulting in an interval-valued polynomial initial condition for the subsequent step. A set of examples is provided.
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