Nonclassical Linear Volterra Equations of the First Kind

Name: Nonclassical Linear Volterra Equations of the First Kind
Brand: De Gruyter
Price: 189.95 EUR
Availability: OnlineOnly

Anatoly S. Apartsyn(Autor*in)

De Gruyter (Verlag)

1. Auflage

Erschienen am 1. März 2011

VI, 168 Seiten

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978-3-11-094497-6 (ISBN)

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Inhalt

Intro
Introduction
Chapter 1. Classical Volterra equations of the first kind
1.1. Classification of integral Volterra equations of the fist kind
1.2. The Gronwall-Bellman lemma
1.3. A difference analog of the Gronwall-Bellman lemma
1.4. Self-regularization
1.5. Two-parametric (a,h)-regularization
1.6. Inequalities with isotone operators
1.7. Inequalities with interchangeable isotone operators
1.8. Unimprovable estimates of solutions of multidimensional integral inequalities
1.9. The well-posedness of a two-dimensional Volterra equation of the first kind
1.10. Unimprovable estimates of solutions of two-dimensional differ¬ence inequalities
Chapter 2. Volterra equations of the first kind with two variable integration limits. The case a(t0) & t0
2.1. Problem statement
2.2. The method of steps
2.3. Illustrative examples
2.4. The existence and uniqueness theorem
2.5. An estimate of the solution stability
2.6. The study of a special problem of mathematical programming
2.7. A numerical solution of the test example
2.8. A geometrical illustration of the reduction by unity in the order of convergence
2.9. A theorem on the convergence of the quadrature method (the general case)
2.10. Some numerical results
2.11. On self-regularization
Chapter 3. Volterra equations of the first kind with two variable limits of integration. The case a(t0) = t0
3.1. Problem statement
3.2. Solution of the simplest test equation
3.3. Existence and uniqueness theorem (the general case)
3.4. Estimation of the solution stability
3.5. Some generalizations of the Gronwall-Bellman inequality
3.6. Numerical solution of a test example
3.7. The proof of convergence for the quadrature method (the general case)
3.8. Some numerical results
3.9. Self-regularization (the case of a disturbance in the right-hand side)
3.10. Stability of a numerical solution with respect to disturbances of a(t)
3.11. Multidimensional Volterra equations of the first kind related to the modelling of nonlinear dynamic systems using the Volterra series
Bibliography
Index

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