Application of Splines to the Numerical Solution of Two-point Boundary-value Problems PDF Download
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Author: Donald C. Todd
Publisher:
ISBN:
Category : Navier-Stokes equations
Languages : en
Pages : 126
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Book Description
In the search for better methods to solve the Navier-Stokes equations, this is a preliminary test of spline collocation, or the application of spline collocation to solve two-point boundary-value problems. Pertinent spline theory and the spline collocation method are developed from first principles. The problems considered are nonlinear, third-order, ordinary differential equations. A FORTRAN IV computer program to solve such problems is described, and a source deck listing is included. Several sample problems solved by the program are presented. (Author).
Author: Donald C. Todd
Publisher:
ISBN:
Category : Navier-Stokes equations
Languages : en
Pages : 126
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Book Description
In the search for better methods to solve the Navier-Stokes equations, this is a preliminary test of spline collocation, or the application of spline collocation to solve two-point boundary-value problems. Pertinent spline theory and the spline collocation method are developed from first principles. The problems considered are nonlinear, third-order, ordinary differential equations. A FORTRAN IV computer program to solve such problems is described, and a source deck listing is included. Several sample problems solved by the program are presented. (Author).
Author:
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
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Book Description
In the search for better methods to solve the Navier-Stokes equations, this is a preliminary test of spline collocation, or the application of spline collocation to solve two-point boundary-value problems. Pertinent spline theory and the spline collocation method are developed from first principles. The problems considered are nonlinear, third-order, ordinary differential equations. A FORTRAN IV computer program to solve such problems is described, and a source deck listing is included. Several sample problems solved by the program are presented. (Author).
Author: J. H. Ahlberg
Publisher: Elsevier
ISBN: 1483222950
Category : Mathematics
Languages : en
Pages : 297
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Book Description
The Theory of Splines and Their Applications discusses spline theory, the theory of cubic splines, polynomial splines of higher degree, generalized splines, doubly cubic splines, and two-dimensional generalized splines. The book explains the equations of the spline, procedures for applications of the spline, convergence properties, equal-interval splines, and special formulas for numerical differentiation or integration. The text explores the intrinsic properties of cubic splines including the Hilbert space interpretation, transformations defined by a mesh, and some connections with space technology concerning the payload of a rocket. The book also discusses the theory of polynomial splines of odd degree which can be approached through algebraically (which depends primarily on the examination in detail of the linear system of equations defining the spline). The theory can also be approached intrinsically (which exploits the consequences of basic integral relations existing between functions and approximating spline functions). The text also considers the second integral relation, raising the order of convergence, and the limits on the order of convergence. The book will prove useful for mathematicians, physicist, engineers, or academicians in the field of technology and applied mathematics.
Author: CARL-WILHELM REINHOLD DE BOOR
Publisher:
ISBN:
Category : Boundary value problems
Languages : en
Pages : 66
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Book Description
Author: Herbert B. Keller
Publisher: SIAM
ISBN: 0898710219
Category : Mathematics
Languages : en
Pages : 67
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Book Description
Lectures on a unified theory of and practical procedures for the numerical solution of two point boundary-value problems.
Author: Carl-Wilhelm Reinhold De Boor
Publisher:
ISBN:
Category : Boundary value problems
Languages : en
Pages : 122
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Book Description
Author: Herbert B. Keller
Publisher: Courier Dover Publications
ISBN: 0486828344
Category : Mathematics
Languages : en
Pages : 417
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Book Description
Elementary yet rigorous, this concise treatment is directed toward students with a knowledge of advanced calculus, basic numerical analysis, and some background in ordinary differential equations and linear algebra. 1968 edition.
Author: P. M. Prenter
Publisher: Courier Corporation
ISBN: 0486783499
Category : Mathematics
Languages : en
Pages : 338
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Book Description
One of the clearest available introductions to variational methods, this text requires only a minimal background in calculus and linear algebra. Its self-contained treatment explains the application of theoretic notions to the kinds of physical problems that engineers regularly encounter. The text’s first half concerns approximation theoretic notions, exploring the theory and computation of one- and two-dimensional polynomial and other spline functions. Later chapters examine variational methods in the solution of operator equations, focusing on boundary value problems in one and two dimensions. Additional topics include least squares and other Galerkin methods. Many helpful definitions, examples, and exercises appear throughout the book. A classic reference in spline theory, this volume will benefit experts as well as students of engineering and mathematics.
Author: Michael Golomb
Publisher:
ISBN:
Category : Approximation theory
Languages : en
Pages : 52
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Book Description
An optimal numerical method is given for the solution of linear two-point boundary value problems. (Author).
Author: Uri M. Ascher
Publisher: SIAM
ISBN: 9781611971231
Category : Mathematics
Languages : en
Pages : 620
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Book Description
This book is the most comprehensive, up-to-date account of the popular numerical methods for solving boundary value problems in ordinary differential equations. It aims at a thorough understanding of the field by giving an in-depth analysis of the numerical methods by using decoupling principles. Numerous exercises and real-world examples are used throughout to demonstrate the methods and the theory. Although first published in 1988, this republication remains the most comprehensive theoretical coverage of the subject matter, not available elsewhere in one volume. Many problems, arising in a wide variety of application areas, give rise to mathematical models which form boundary value problems for ordinary differential equations. These problems rarely have a closed form solution, and computer simulation is typically used to obtain their approximate solution. This book discusses methods to carry out such computer simulations in a robust, efficient, and reliable manner.
