A Domain-Theoretic Account of Picard's Theorem

DOI10.1112/S1461157000001315zbMath1112.65065OpenAlexW3020998446MaRDI QIDQ3430832

Dirk Pattinson, Abbas Edalat

Publication date: 4 April 2007

Published in: LMS Journal of Computation and Mathematics (Search for Journal in Brave)

Full work available at URL: http://www.lms.ac.uk/jcm/10/lms2005-056/

zbMATH Keywords

iterative algorithminitial value problemsvector fieldsalgebraic complexityLipschitz conditionspeed of convergencerational arithmetic

Mathematics Subject Classification ID

Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations (34A12) Numerical methods for initial value problems involving ordinary differential equations (65L05) Continuous lattices and posets, applications (06B35)

Related Items (6)

Domain theoretic second-order Euler's method for solving initial value problems ⋮ Recursive solution of initial value problems with temporal discretization ⋮ A domain-theoretic framework for robustness analysis of neural networks ⋮ A differential operator and weak topology for Lipschitz maps ⋮ Computability of Differential Equations ⋮ Enclosing the behavior of a hybrid automaton up to and beyond a Zeno point

Cites Work

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• Validated solutions of initial value problems for ordinary differential equations
• The primitive recursive analysis of ordinary differential equations and the complexity of their solutions
• On the computational complexity of ordinary differential equations
• A computable ordinary differential equation which possesses no computable solution
• Domain theory and differential calculus (functions of one variable)
• Continuous Lattices and Domains

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