Spline Collocation Approximations To Solutions Of A Class Of Boundary Value Problems For Partial Differential Equations Which Arise In Control Theory
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Spline Collocation Approximations To Solutions Of A Class Of Boundary Value Problems For Partial Differential Equations Which Arise In Control Theory
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Author : Wayne Wilroy Wallace
language : en
Publisher:
Release Date : 1975
Spline Collocation Approximations To Solutions Of A Class Of Boundary Value Problems For Partial Differential Equations Which Arise In Control Theory written by Wayne Wilroy Wallace and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1975 with categories.
On The Approximate Solution Of Linear Boundary Value Problems By Collocation Methods Using Smooth Spline Functions
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Author : Sigrid Spettmann-Lukassen
language : de
Publisher:
Release Date : 1984
On The Approximate Solution Of Linear Boundary Value Problems By Collocation Methods Using Smooth Spline Functions written by Sigrid Spettmann-Lukassen and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984 with categories.
Spline Approximations To The Solutions Of Two Point Boundary Value Problems
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Author : Michael Golomb
language : en
Publisher:
Release Date : 1971
Spline Approximations To The Solutions Of Two Point Boundary Value Problems written by Michael Golomb and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1971 with Approximation theory categories.
An optimal numerical method is given for the solution of linear two-point boundary value problems. (Author).
Extrapolation With Spline Collocation Methods For Two Point Boundary Value Problems I Justifications And Proposals
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Author : James W. Daniel
language : en
Publisher:
Release Date : 1974
Extrapolation With Spline Collocation Methods For Two Point Boundary Value Problems I Justifications And Proposals written by James W. Daniel and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1974 with Numerical analysis categories.
Extrapolation With Spline Collocation Methods For Two Point Boundary Value Problems 1 Justifications And Proposals
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Author : J. W. Daniel
language : en
Publisher:
Release Date : 1974
Extrapolation With Spline Collocation Methods For Two Point Boundary Value Problems 1 Justifications And Proposals written by J. W. Daniel and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1974 with categories.
Spline Approximations To The Solution Of Two Point Boundary Value Problems
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Author : Michael Golomb
language : en
Publisher:
Release Date : 1971
Spline Approximations To The Solution Of Two Point Boundary Value Problems written by Michael Golomb and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1971 with categories.
Splines And Variational Methods
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Author : P. M. Prenter
language : en
Publisher: Courier Corporation
Release Date : 2008-01-01
Splines And Variational Methods written by P. M. Prenter and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-01-01 with Mathematics categories.
One of the clearest available introductions to variational methods, this text requires only a minimal background in linear algebra and analysis. It explains the application of theoretic notions to the kinds of physical problems that engineers regularly encounter. Many helpful definitions, examples, and exercises appear throughout the book. 1975 edition.
Solving Boundary Value Problems With A Spline Collocation Code
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Author : U. Ascher
language : en
Publisher:
Release Date : 1978
Solving Boundary Value Problems With A Spline Collocation Code written by U. Ascher and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1978 with categories.
Quartic Spline Collocation Methods For Second Order Two Point Boundary Value Ode Problems
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Author : Guohong Liu
language : en
Publisher:
Release Date : 2007
Quartic Spline Collocation Methods For Second Order Two Point Boundary Value Ode Problems written by Guohong Liu and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with categories.
Collocation methods based on quartic splines are presented for second-order two-point boundary value problems. In addition to the boundary conditions specified by the problem, extra boundary conditions are introduced in order to uniquely determine the quartic spline approximation. The standard quartic spline collocation method gives fourth order bounds. Two optimal methods, namely the extrapolated (one-step) and the deferred-correction (two-step) methods, are formulated based on appropriate extra boundary conditions and an appropriate perturbation of the operators of the differential equation, boundary conditions and extra boundary conditions. The convergence analysis and error bounds are developed using a Green's functions approach. The analysis shows that the maximum discrete error is of sixth order, and the maximum global error is of fifth order for the optimal methods.The properties of the matrices arising from the optimal methods for a certain class of problems are studied. Non-optimal collocation methods based on different extra boundary conditions are also investigated. Problems with layers are also considered, and a grid refinement technique is presented. The theoretical behavior of the collocation methods is verified by numerical results.
Quartic Spline Collocation Methods For Fourth Order Two Point Boundary Value Problems
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Author : Ying Zhu
language : en
Publisher:
Release Date : 2001
Quartic Spline Collocation Methods For Fourth Order Two Point Boundary Value Problems written by Ying Zhu and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with categories.
This thesis presents numerical methods for the solution of general linear fourth-order boundary value problems in one dimension. The methods are based on quartic splines and the collocation discretization methodology with the midpoints of a uniform partition being the collocation points. The standard quartic-spline collocation method is second order. Two sixth-order quartic-spline collocation methods are developed and analyzed. They are both based on a high order perturbation of the differential equation and boundary conditions operators. The error analysis follows the Green's function approach and shows that both methods exhibit optimal order of convergence, that is, they are locally sixth order on the gridpoints and midpoints, and fifth order globally. The properties of the matrices arising from a restricted class of problems are studied. Analytic formulae for the eigenvalues and eigenvectors are developed. Numerical results verify the orders of convergence predicted by analysis.