Nonclassical Linear Volterra Equations of the First Kind
VSP International Science Publishers (Verlag)
978-90-6764-375-7 (ISBN)
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Anatoly S. Apartsyn, L. A. Melentiev Institute of Energy Systems, Russian Academy of Sciences, Irkutsk, Russia.
Introduction
Classical Volterra equations of the first kind
Classification of integral Volterra equations of the first kind
The Gronwall-Bellman lemma
A difference analog of the Gronwall-Bellman lemma
Self-regularization
Two-parametric (a, h)-regularization
Inequalities with isotone operators
Inequalities with interchangeable isotone operators
Unimprovable estimates of solutions of multidimensional integral inequalities
The well-posedness of a two-dimensional Volterra Equation of the first kind
Unimprovable estimates of solutions for two-dimensional difference inequalities
Volterra equations of the first kind with two variable integration limits. The case a(t0) < t0
Problem statement
The method of steps
Illustrative examples
The existence and uniqueness theorem
An estimate of the solution stability
The study of a special problem of mathematical programming
A numerical solution of the test example
A geometrical illustration of the reduction by unity in the order of convergence
A theorem on the convergence of the quadrature method (the general case)
Some numerical results
On self-regularization
Volterra equations of the first kind with two variable limits of integration. The case a(t0) = t0
Problem statement
Solution of the simplest test equation
Existence and uniqueness theorem (the general case)
Estimation of the solution stability
Some generalizations of the Gronwall-Bellman inequality
Numerical solution of a test example
The proof of convergence for the quadrature method (the general case)
Some numerical results
Self-regularization (the case of a disturbance in the right-hand side)
Stability of a numerical solution with resepect to disturbances of a(t)
Multidimensional Volterra equations of the first kind related to the modelling of nonlinear dynamic systems using the Volterra series
Bibliography
Index
| Erscheint lt. Verlag | 23.6.2003 |
|---|---|
| Reihe/Serie | Inverse and Ill-Posed Problems Series |
| Verlagsort | Zeist |
| Sprache | englisch |
| Maße | 155 x 230 mm |
| Gewicht | 455 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Angewandte Mathematik |
| ISBN-10 | 90-6764-375-0 / 9067643750 |
| ISBN-13 | 978-90-6764-375-7 / 9789067643757 |
| Zustand | Neuware |
| Informationen gemäß Produktsicherheitsverordnung (GPSR) | |
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