Spline Solutions Of High 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.
Boundary Value Problems From Higher Order Differential Equations
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Author : Ravi P Agarwal
language : en
Publisher: World Scientific
Release Date : 1986-07-01
Boundary Value Problems From Higher Order Differential Equations written by Ravi P Agarwal and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986-07-01 with Mathematics categories.
Contents: Some ExamplesLinear ProblemsGreen's FunctionMethod of Complementary FunctionsMethod of AdjointsMethod of ChasingSecond Order EquationsError Estimates in Polynomial InterpolationExistence and UniquenessPicard's and Approximate Picard's MethodQuasilinearization and Approximate QuasilinearizationBest Possible Results: Weight Function TechniqueBest Possible Results: Shooting MethodsMonotone Convergence and Further ExistenceUniqueness Implies ExistenceCompactness Condition and Generalized SolutionsUniqueness Implies UniquenessBoundary Value FunctionsTopological MethodsBest Possible Results: Control Theory MethodsMatching MethodsMaximal SolutionsMaximum PrincipleInfinite Interval ProblemsEquations with Deviating Arguments Readership: Graduate students, numerical analysts as well as researchers who are studying open problems. Keywords:Boundary Value Problems;Ordinary Differential Equations;Green's Function;Quasilinearization;Shooting Methods;Maximal Solutions;Infinite Interval Problems
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).
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.
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.
High Order Two Point Boundary Value Problems
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Author : Samaher M. Yasein
language : en
Publisher: LAP Lambert Academic Publishing
Release Date : 2014-02
High Order Two Point Boundary Value Problems written by Samaher M. Yasein 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 2014-02 with categories.
The aim of this book is to present method for solving higher order non - linear two point boundary value problems for ordinary differential equations of the different kinds of the boundary conditions, we propose semi-analytic technique using repeated interpolation to construct polynomial solution. Also, we discussion the existence and uniqueness of solutions. Many examples are presented to demonstrate the applicability, accuracy and efficiency of the methods on one hand and to confirm the convergence on the other hand.
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.