On the computational complexity of ordinary differential equations
Information and Control
Handbook of logic in computer science (vol. 3)
A first course in the numerical analysis of differential equations
A first course in the numerical analysis of differential equations
Some recent advances in validated methods for IVPs for ODEs
Applied Numerical Mathematics
Methods and Applications of Interval Analysis (SIAM Studies in Applied and Numerical Mathematics) (Siam Studies in Applied Mathematics, 2.)
Time Complexity and Convergence Analysis of Domain Theoretic Picard Method
WoLLIC '08 Proceedings of the 15th international workshop on Logic, Language, Information and Computation
Domain Theoretic Solutions of Initial Value Problems for Unbounded Vector Fields
Electronic Notes in Theoretical Computer Science (ENTCS)
A computational model for multi-variable differential calculus
Information and Computation
Hi-index | 0.00 |
This paper presents a method of solving initial value problems using Euler's method, based on the domain of interval valued functions of a real variable. In contrast to other interval based techniques, the actual computation of enclosures to the solution is not based on the code list (term representation) of the vector field that defines the equation, but assumes instead that the vector field is approximated to an arbitrary degree of accuracy. By using approximations defined over rational or dyadic numbers, we obtain proper data types for approximating both the vector field and the solution. As a consequence, we can guarantee the speed of convergence also for an implementation of the method. Furthermore, we give estimates on the algebraic complexity for computing approximate solutions.