A Comparison of Some Numerical Methods for Solving Volterra Integral Equations PDF Download
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Author: Scotty Glen Houston
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
We implement several methods for solving Volterra integral equations based on standard techniques for solving ordinary differential equations. In particular we implement a version of the modified Euler method,we implement the standard fourth order Runge-Kutta method.We compare these with a novel collocation method using Bernstein polynomials.We also look at Volterra integral equations with weakly singular kernels. Here the standard methods developed above do not apply though the collocation method can still be used. We develop two “product integration” methods, derived from numerical integration methods that can be applied to these weakly singular Volterra integral equations and compare them to the collocation method.
Author: Scotty Glen Houston
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
We implement several methods for solving Volterra integral equations based on standard techniques for solving ordinary differential equations. In particular we implement a version of the modified Euler method,we implement the standard fourth order Runge-Kutta method.We compare these with a novel collocation method using Bernstein polynomials.We also look at Volterra integral equations with weakly singular kernels. Here the standard methods developed above do not apply though the collocation method can still be used. We develop two “product integration” methods, derived from numerical integration methods that can be applied to these weakly singular Volterra integral equations and compare them to the collocation method.
Author: Peter Linz
Publisher: SIAM
ISBN: 9781611970852
Category : Mathematics
Languages : en
Pages : 240
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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.
Author: Peter Linz
Publisher:
ISBN:
Category : Boundary value problems
Languages : en
Pages : 354
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Book Description
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: Michael A. Golberg
Publisher: Springer Science & Business Media
ISBN: 1489925937
Category : Mathematics
Languages : en
Pages : 428
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Book Description
In 1979, I edited Volume 18 in this series: Solution Methods for Integral Equations: Theory and Applications. Since that time, there has been an explosive growth in all aspects of the numerical solution of integral equations. By my estimate over 2000 papers on this subject have been published in the last decade, and more than 60 books on theory and applications have appeared. In particular, as can be seen in many of the chapters in this book, integral equation techniques are playing an increas ingly important role in the solution of many scientific and engineering problems. For instance, the boundary element method discussed by Atkinson in Chapter 1 is becoming an equal partner with finite element and finite difference techniques for solving many types of partial differential equations. Obviously, in one volume it would be impossible to present a complete picture of what has taken place in this area during the past ten years. Consequently, we have chosen a number of subjects in which significant advances have been made that we feel have not been covered in depth in other books. For instance, ten years ago the theory of the numerical solution of Cauchy singular equations was in its infancy. Today, as shown by Golberg and Elliott in Chapters 5 and 6, the theory of polynomial approximations is essentially complete, although many details of practical implementation remain to be worked out.
Author: Peter Linz
Publisher:
ISBN:
Category : Integral equations
Languages : en
Pages : 97
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Book Description
Theoretical and practical aspects of numerical methods for solving Volterra integral equations of the first and second kinds are studied. (Author).
Author: Abdul-majid Wazwaz
Publisher: World Scientific Publishing Company
ISBN: 9813105089
Category : Mathematics
Languages : en
Pages : 224
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Book Description
This book presents the subject of integral equations in an accessible manner for a variety of applications. Emphasis is placed on understanding the subject while avoiding the abstract and compact theorems. A distinctive feature of the book is that it introduces the recent powerful and reliable developments in this field, which are not covered in traditional texts. The newly developed decomposition method, the series solution method and the direct computation method are thoroughly implemented, which allows the topic to be far more accessible. The book also includes some of the traditional techniques for comparison.Using the newly developed methods, the author successfully handles Fredholm and Volterra integral equations, singular integral equations, integro-differential equations and nonlinear integral equations, with promising results for linear and nonlinear models. Many examples are given to introduce the material in a clear and thorough fashion. In addition, many exercises are provided to build confidence, ease and skill in using the new methods.This book may be used as a text for advanced undergraduates and graduate students in mathematics and scientific areas, and as a work of reference for research study of differential equations and numerical analysis.
Author: Harendra Singh
Publisher: Springer Nature
ISBN: 3030655091
Category : Technology & Engineering
Languages : en
Pages : 255
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Book Description
This book includes different topics associated with integral and integro-differential equations and their relevance and significance in various scientific areas of study and research. Integral and integro-differential equations are capable of modelling many situations from science and engineering. Readers should find several useful and advanced methods for solving various types of integral and integro-differential equations in this book. The book is useful for graduate students, Ph.D. students, researchers and educators interested in mathematical modelling, applied mathematics, applied sciences, engineering, etc. Key Features • New and advanced methods for solving integral and integro-differential equations • Contains comparison of various methods for accuracy • Demonstrates the applicability of integral and integro-differential equations in other scientific areas • Examines qualitative as well as quantitative properties of solutions of various types of integral and integro-differential equations
Author: M. A. Goldberg
Publisher: Springer Science & Business Media
ISBN: 1475714661
Category : Science
Languages : en
Pages : 351
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Book Description
Author: John Alan Belward
Publisher:
ISBN:
Category : Integral equations
Languages : en
Pages : 16
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Book Description
