Author: Fan Bo
Publisher:
ISBN:
Category : Collocation methods
Languages : en
Pages : 190

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Author: Fan Bai
Publisher:
ISBN:
Category : Collocation methods
Languages : en
Pages : 0

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Author: Hermann Brunner
Publisher: Cambridge University Press
ISBN: 9780521806152
Category : Mathematics
Languages : en
Pages : 620

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Author: Henry Ekah-Kunde
Publisher: GRIN Verlag
ISBN: 3668484260
Category : Mathematics
Languages : en
Pages : 26

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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.

Author: Hermann Brunner
Publisher: Cambridge University Press
ISBN: 1107098726
Category : Mathematics
Languages : en
Pages : 405

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Author: Herman J. J. te Riele
Publisher:
ISBN:
Category :
Languages : en
Pages : 19

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Author: Herman H. Riele
Publisher:
ISBN:
Category :
Languages : en
Pages : 19

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Author:
Publisher:
ISBN:
Category :
Languages : en
Pages : 5

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Nonlinear Volterra integral equation with weakly singular kernels are considered and are solved by applying piecewise collocation methods based on multiquadric approximations combined with Gauss quadrature rules.

Author: Hermann Brunner
Publisher: North Holland
ISBN:
Category : Mathematics
Languages : en
Pages : 608

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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.

Author: Jie Shen
Publisher: Springer Science & Business Media
ISBN: 3540710418
Category : Mathematics
Languages : en
Pages : 481

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Book Description
Along with finite differences and finite elements, spectral methods are one of the three main methodologies for solving partial differential equations on computers. This book provides a detailed presentation of basic spectral algorithms, as well as a systematical presentation of basic convergence theory and error analysis for spectral methods. Readers of this book will be exposed to a unified framework for designing and analyzing spectral algorithms for a variety of problems, including in particular high-order differential equations and problems in unbounded domains. The book contains a large number of figures which are designed to illustrate various concepts stressed in the book. A set of basic matlab codes has been made available online to help the readers to develop their own spectral codes for their specific applications.