Author: Herman J. J. te Riele
Publisher:
ISBN:
Category :
Languages : en
Pages : 19
Book Description
Collocation Methods for Weakly Singular Second Kind Volterra Integral Equations with Non-smooth Solution
Author: Herman J. J. te Riele
Publisher:
ISBN:
Category :
Languages : en
Pages : 19
Book Description
Publisher:
ISBN:
Category :
Languages : en
Pages : 19
Book Description
Collocation Methods for Weakly Singular Second Kind Volterra Integral Equations with Non-smooth Solution
Author: Herman H. Riele
Publisher:
ISBN:
Category :
Languages : en
Pages : 19
Book Description
Publisher:
ISBN:
Category :
Languages : en
Pages : 19
Book Description
Collocation Methods for Volterra Integral and Related Functional Differential Equations
Author: Hermann Brunner
Publisher: Cambridge University Press
ISBN: 9780521806152
Category : Mathematics
Languages : en
Pages : 620
Book Description
Publisher Description
Publisher: Cambridge University Press
ISBN: 9780521806152
Category : Mathematics
Languages : en
Pages : 620
Book Description
Publisher Description
Collocation method for Weakly Singular Volterra Integral Equations of the Second Type
Author: Henry Ekah-Kunde
Publisher: GRIN Verlag
ISBN: 3668484260
Category : Mathematics
Languages : en
Pages : 26
Book Description
Seminar paper from the year 2015 in the subject Mathematics - Applied Mathematics, grade: A, , language: English, abstract: In scientific and engineering problems Volterra integral equations are always encountered. Applications of Volterra integral equations arise in areas such as population dynamics, spread of epidemics in the society, etc. The problem statement is to obtain a good numerical solution to such an integral equation. A brief theory of Volterra Integral equation, particularly, of weakly singular types, and a numerical method, the collocation method, for solving such equations, in particular Volterra integral equation of second kind, is handled in this paper. The principle of this method is to approximate the exact solution of the equation in a suitable finite dimensional space. The approximating space considered here is the polynomial spline space. In the treatment of the collocation method emphasis is laid, during discretization, on the mesh type. The approximating space applied here is the polynomial spline space. The discrete convergence properties of spline collocation solutions for certain Volterra integral equations with weakly singular kernels shall is analyzed. The order of convergence of spline collocation on equidistant mesh points is also compared with approximation on graded meshes. In particular, the attainable convergence orders at the collocation points are examined for certain choices of the collocation parameters.
Publisher: GRIN Verlag
ISBN: 3668484260
Category : Mathematics
Languages : en
Pages : 26
Book Description
Seminar paper from the year 2015 in the subject Mathematics - Applied Mathematics, grade: A, , language: English, abstract: In scientific and engineering problems Volterra integral equations are always encountered. Applications of Volterra integral equations arise in areas such as population dynamics, spread of epidemics in the society, etc. The problem statement is to obtain a good numerical solution to such an integral equation. A brief theory of Volterra Integral equation, particularly, of weakly singular types, and a numerical method, the collocation method, for solving such equations, in particular Volterra integral equation of second kind, is handled in this paper. The principle of this method is to approximate the exact solution of the equation in a suitable finite dimensional space. The approximating space considered here is the polynomial spline space. In the treatment of the collocation method emphasis is laid, during discretization, on the mesh type. The approximating space applied here is the polynomial spline space. The discrete convergence properties of spline collocation solutions for certain Volterra integral equations with weakly singular kernels shall is analyzed. The order of convergence of spline collocation on equidistant mesh points is also compared with approximation on graded meshes. In particular, the attainable convergence orders at the collocation points are examined for certain choices of the collocation parameters.
Volterra Integral Equations
Author: Hermann Brunner
Publisher: Cambridge University Press
ISBN: 1316982653
Category : Mathematics
Languages : en
Pages : 405
Book Description
This book offers a comprehensive introduction to the theory of linear and nonlinear Volterra integral equations (VIEs), ranging from Volterra's fundamental contributions and the resulting classical theory to more recent developments that include Volterra functional integral equations with various kinds of delays, VIEs with highly oscillatory kernels, and VIEs with non-compact operators. It will act as a 'stepping stone' to the literature on the advanced theory of VIEs, bringing the reader to the current state of the art in the theory. Each chapter contains a large number of exercises, extending from routine problems illustrating or complementing the theory to challenging open research problems. The increasingly important role of VIEs in the mathematical modelling of phenomena where memory effects play a key role is illustrated with some 30 concrete examples, and the notes at the end of each chapter feature complementary references as a guide to further reading.
Publisher: Cambridge University Press
ISBN: 1316982653
Category : Mathematics
Languages : en
Pages : 405
Book Description
This book offers a comprehensive introduction to the theory of linear and nonlinear Volterra integral equations (VIEs), ranging from Volterra's fundamental contributions and the resulting classical theory to more recent developments that include Volterra functional integral equations with various kinds of delays, VIEs with highly oscillatory kernels, and VIEs with non-compact operators. It will act as a 'stepping stone' to the literature on the advanced theory of VIEs, bringing the reader to the current state of the art in the theory. Each chapter contains a large number of exercises, extending from routine problems illustrating or complementing the theory to challenging open research problems. The increasingly important role of VIEs in the mathematical modelling of phenomena where memory effects play a key role is illustrated with some 30 concrete examples, and the notes at the end of each chapter feature complementary references as a guide to further reading.
Collocation Methods for Weakly Singular Volterra Integral Equations with Vanishing Delays
Author: Fan Bai
Publisher:
ISBN:
Category : Collocation methods
Languages : en
Pages : 190
Book Description
Publisher:
ISBN:
Category : Collocation methods
Languages : en
Pages : 190
Book Description
The Numerical Solution of Volterra Equations
Author: Hermann Brunner
Publisher: North Holland
ISBN:
Category : Mathematics
Languages : en
Pages : 608
Book Description
This monograph presents the theory and modern numerical analysis of Volterra integral and integro-differential equations, including equations with weakly singular kernels. While the research worker will find an up-to-date account of recent developments of numerical methods for such equations, including an extensive bibliography, the authors have tried to make the book accessible to the non-specialist possessing only a limited knowledge of numerical analysis. After an introduction to the theory of Volterra equations and to numerical integration, the book covers linear methods and Runge-Kutta methods, collocation methods based on polynomial spline functions, stability of numerical methods, and it surveys computer programs for Volterra integral and integro-differential equations.
Publisher: North Holland
ISBN:
Category : Mathematics
Languages : en
Pages : 608
Book Description
This monograph presents the theory and modern numerical analysis of Volterra integral and integro-differential equations, including equations with weakly singular kernels. While the research worker will find an up-to-date account of recent developments of numerical methods for such equations, including an extensive bibliography, the authors have tried to make the book accessible to the non-specialist possessing only a limited knowledge of numerical analysis. After an introduction to the theory of Volterra equations and to numerical integration, the book covers linear methods and Runge-Kutta methods, collocation methods based on polynomial spline functions, stability of numerical methods, and it surveys computer programs for Volterra integral and integro-differential equations.
Volterra-type integral equations of the second kind with non-smooth solutions
Author: H. Brunner
Publisher:
ISBN:
Category :
Languages : en
Pages : 20
Book Description
Publisher:
ISBN:
Category :
Languages : en
Pages : 20
Book Description
Collocation Methods for Weakly Singular Volterra Integral Equations with Vanishing Delays
Author: Fan Bo
Publisher:
ISBN:
Category : Collocation methods
Languages : en
Pages : 190
Book Description
Publisher:
ISBN:
Category : Collocation methods
Languages : en
Pages : 190
Book Description
Analytical and Numerical Methods for Volterra Equations
Author: Peter Linz
Publisher: SIAM
ISBN: 9781611970852
Category : Mathematics
Languages : en
Pages : 240
Book Description
Presents an aspect of activity in integral equations methods for the solution of Volterra equations for those who need to solve real-world problems. Since there are few known analytical methods leading to closed-form solutions, the emphasis is on numerical techniques. The major points of the analytical methods used to study the properties of the solution are presented in the first part of the book. These techniques are important for gaining insight into the qualitative behavior of the solutions and for designing effective numerical methods. The second part of the book is devoted entirely to numerical methods. The author has chosen the simplest possible setting for the discussion, the space of real functions of real variables. The text is supplemented by examples and exercises.
Publisher: SIAM
ISBN: 9781611970852
Category : Mathematics
Languages : en
Pages : 240
Book Description
Presents an aspect of activity in integral equations methods for the solution of Volterra equations for those who need to solve real-world problems. Since there are few known analytical methods leading to closed-form solutions, the emphasis is on numerical techniques. The major points of the analytical methods used to study the properties of the solution are presented in the first part of the book. These techniques are important for gaining insight into the qualitative behavior of the solutions and for designing effective numerical methods. The second part of the book is devoted entirely to numerical methods. The author has chosen the simplest possible setting for the discussion, the space of real functions of real variables. The text is supplemented by examples and exercises.