Spline Solutions Of Higher Order Boundary Value Problems
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Spline Solutions Of Higher Order Boundary Value Problems
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Author : Parcha Kalyani
language : en
Publisher: GRIN Verlag
Release Date : 2020-06-09
Spline Solutions Of Higher Order Boundary Value Problems written by Parcha Kalyani and has been published by GRIN Verlag this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-06-09 with Mathematics categories.
Doctoral Thesis / Dissertation from the year 2014 in the subject Mathematics - Applied Mathematics, , language: English, abstract: Some of the problems of real world phenomena can be described by differential equations involving the ordinary or partial derivatives with some initial or boundary conditions. To interpret the physical behavior of the problem it is necessary to know the solution of the differential equation. Unfortunately, it is not possible to solve some of the differential equations whether they are ordinary or partial with initial or boundary conditions through the analytical methods. When, we fail to find the solution of ordinary differential equation or partial differential equation with initial or boundary conditions through the analytical methods, one can obtain the numerical solution of such problems through the numerical methods up to the desired degree of accuracy. Of course, these numerical methods can also be applied to find the numerical solution of a differential equation which can be solved analytically. Several problems in natural sciences, social sciences, medicine, business management, engineering, particle dynamics, fluid mechanics, elasticity, heat transfer, chemistry, economics, anthropology and finance can be transformed into boundary value problems using mathematical modeling. A few problems in various fields of science and engineering yield linear and nonlinear boundary value problems of second order such as heat equation in thermal studies, wave equation in communication etc. Fifth-order boundary value problems generally arise in mathematical modeling of viscoelastic flows. The dynamo action in some stars may be modeled by sixth-order boundary-value problems. The narrow convecting layers bounded by stable layers which are believed to surround A-type stars may be modeled by sixth-order boundary value problems which arise in astrophysics. The seventh order boundary value problems generally arise in modeling induction motors with two rotor circuits. Various phenomena such as convection, flow in wind tunnels, lee waves, eddies, etc. can also be modeled by higher order boundary value problems.
Spline Solutions Of High Order Boundary Value Problems
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Author : Shahid S. Siddiqi
language : en
Publisher:
Release Date : 1994
Spline Solutions Of High Order Boundary Value Problems written by Shahid S. Siddiqi and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with categories.
Higher Order Numerical Solutions Using Cubic Splines
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Author : S. G. Rubin
language : en
Publisher:
Release Date : 1976
Higher Order Numerical Solutions Using Cubic Splines written by S. G. Rubin and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1976 with Differential equations, Partial categories.
Splines And Variational Methods
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Author : P. M. Prenter
language : en
Publisher: Courier Corporation
Release Date : 2013-11-26
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 2013-11-26 with Mathematics categories.
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.
Application Of Splines To The Numerical Solution Of Two Point Boundary Value Problems
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Author : Donald C. Todd
language : en
Publisher:
Release Date : 1978
Application Of Splines To The Numerical Solution Of Two Point Boundary Value Problems written by Donald C. Todd and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1978 with Navier-Stokes equations categories.
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).
Boundary Value Problems For Higher Order Differential Equations
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Author : Ravi P. Agarwal
language : en
Publisher:
Release Date : 1979
Boundary Value Problems For Higher Order Differential Equations written by Ravi P. Agarwal and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1979 with Boundary value problems categories.
Numerical Treatment Of Boundary Value Problems Using Spline Functions
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Author : Waheed Zahra
language : en
Publisher: LAP Lambert Academic Publishing
Release Date : 2010-12
Numerical Treatment Of Boundary Value Problems Using Spline Functions written by Waheed Zahra and has been published by LAP Lambert Academic Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-12 with categories.
Nonpolynomial Spline Methods (NPSMs) are presented for solving single and system of boundary value problems (BVPs) of orders two, four, six and an 2mth order BVPs respectively. Also, the numerical solution of singular second order BVPs is considered. Optimal order approximations to the solutions of these boundary value problems are obtained. The matrix properties of these BVPs, arising from the discretization of systems of BVPs by NPSMs, are discussed. Sufficient conditions for the optimal convergence for NPSMs are obtained. Also, NPSMs generalize other recent finite difference methods and polynomial spline methods through arbitrary choices of some defined parameters in these methods. Numerical results demonstrated by the NPSMs are shown to produce smaller approximation errors and the superiority of our methods over other recent methods such as finite difference methods, polynomial spline methods and spline collocation methods. These new proposed methods are very encouraging in dealing with boundary value problems.
The Theory Of Splines And Their Applications
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Author : J. H. Ahlberg
language : en
Publisher: Elsevier
Release Date : 2016-06-03
The Theory Of Splines And Their Applications written by J. H. Ahlberg and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-06-03 with Mathematics categories.
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.
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.
The Numerical Solution Of Differential And Integral Equations By Spline Functions
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Author : Hing Sum Hung
language : en
Publisher:
Release Date : 1970
The Numerical Solution Of Differential And Integral Equations By Spline Functions written by Hing Sum Hung and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1970 with Boundary value problems categories.
Spline function methods are developed for the numerical solution of initial-value and boundary-value problems for ordinary differential equations, and for Volterra integral and integro differential equations. Asymptotic error formulae are developed and numerical examples are given. (Author).