Results 1 
2 of
2
Constructive Analysis with Witnesses
"... Contents 1. Real Numbers 3 2 3 1.2. Reals, Equality of Reals 5 1.3. The Archimedian Axiom 6 1.4. Nonnegative and Positive Reals 6 1.5. Arithmetical Functions 7 1.6. Comparison of Reals 8 1.7. NonCountability 10 1.8. Cleaning of Reals 11 2. Sequences and Series of Real Numbers 11 2.1. Completenes ..."
Abstract

Cited by 4 (1 self)
 Add to MetaCart
Contents 1. Real Numbers 3 2 3 1.2. Reals, Equality of Reals 5 1.3. The Archimedian Axiom 6 1.4. Nonnegative and Positive Reals 6 1.5. Arithmetical Functions 7 1.6. Comparison of Reals 8 1.7. NonCountability 10 1.8. Cleaning of Reals 11 2. Sequences and Series of Real Numbers 11 2.1. Completeness 11 2.2. Limits and Inequalities 13 2.3. Series 13 2.4. Redundant Dyadic Representation of Reals 14 2.5. Convergence Tests 15 2.6. Reordering Theorem 17 2.7. The Exponential Series 18 3. The Exponential Function for Complex Numbers 21 4. Continuous Functions 23 4.1. Suprema and In ma 24 4.2. Continuous Functions 25 4.3. Application of a Continuous Function to a Real 27 4.4. Continuous Functions and Limits 28 4.5. Composition of Continuous Functions 28 4.6. Properties of Continuous Functions 29 4.7. Intermediate Value Theorem 30 4.8. Continuity of Functions with More Than One Variable 32 5. Dierentiation 33 5.1. Derivatives 33 5.2. Bounds on the Slope 33 5.3. Properties of Derivatives 34 5
Initial Value Problems in Domain Theory
"... We present a domaintheoretic version of the Picard operator and of Picard's theorem for solving classical initial value problems. Our formulation of the Picard operator allows us to compute solutions as least xed points on the space of Scott continuous intervalvalued maps of a real variab ..."
Abstract
 Add to MetaCart
We present a domaintheoretic version of the Picard operator and of Picard's theorem for solving classical initial value problems. Our formulation of the Picard operator allows us to compute solutions as least xed points on the space of Scott continuous intervalvalued maps of a real variable. In this setup, which considerably simplies earlier approaches, we obtain fast convergence to the solution, given that the vector eld is Lipschitz and can be approximated by step functions.