| Titre : | The Numerical Solution of Nonlinear Weakly Singular Volterra Integral Equations |
| Auteurs : | Ahlem NEMER, Auteur ; Zouhir Mokhtari, Directeur de thèse |
| Type de document : | Monographie imprimée |
| Editeur : | Biskra [Algérie] : Faculté des Sciences Exactes et des Sciences de la Nature et de la Vie, Université Mohamed Khider, 2021 |
| Format : | 1 vol. (70 p.) / ill., couv. ill. en coul / 30 cm |
| Langues: | Anglais |
| Mots-clés: | Volterra integral equation, product integration method, weakly singular kernel |
| Résumé : |
This thesis is intended to solve Volterra integral equations. More precisely, it focuses on the cases of a weakly singular kernel. These integral equations can be solvable when we use the product integration method that plays an important role. For simplicity, we begin this thesis by giving some elementary concepts and basic theories. |
| Sommaire : |
Contents Dedication i Acknowledgements ii Symbols 1 Abstract 2 Introduction 4 1 Discussion of basic theories for Volterra integral equations 8 1.1 Review of various classes of Volterra integral equations . . . . . . . . . . . . . . 8 1.1.1 First−kind Volterra integral equations . . . . . . . . . . . . . . . . . . . 9 1.1.2 Second−kind Volterra integral equations . . . . . . . . . . . . . . . . . . 10 1.2 Convergence of Broyden's method . . . . . . . . . . . . . . . . . . . . . . . . . . 12 1.3 Polynomial approximations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 1.3.1 Hermite−Fejér interpolation polynomials . . . . . . . . . . . . . . . . . . 16 1.3.2 Piecewise linear interpolation . . . . . . . . . . . . . . . . . . . . . . . . 17 iiiContents 1.3.3 Bernstein polynomials . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 1.4 Review of bounded linear operators . . . . . . . . . . . . . . . . . . . . . . . . . 19 2 Numerical analysis of integral equations 23 2.1 Solvability of nonlinear Volterra integral equations . . . . . . . . . . . . . . . . 23 2.2 Techniques of a product integration method . . . . . . . . . . . . . . . . . . . . 26 2.3 Convergence details of the product integration method . . . . . . . . . . . . . . 29 3 Application of the product integration method 35 3.1 Solvability of linear Volterra integral equations . . . . . . . . . . . . . . . . . . 36 3.2 Linear systems formed by the product integration method . . . . . . . . . . . . 37 3.3 Convergence analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 4 Numerical applications 45 4.1 Examples of nonlinear Volterra integral equations . . . . . . . . . . . . . . . . . 45 4.2 Examples of linear Volterra integral equations . . . . . . . . . . . . . . . . . . . 52 Conclusion 60 Bibliography 61 |
| En ligne : | http://thesis.univ-biskra.dz/5507/1/th%C3%A8se_math_2021%20.pdf |
Disponibilité (1)
| Cote | Support | Localisation | Statut |
|---|---|---|---|
| TM/114 | Théses de doctorat | bibliothèque sciences exactes | Consultable |
