Spline Solutions Of Higher Order Boundary Value Problems

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Spline Solutions of Higher Order Boundary Value Problems

Author : Parcha Kalyani
Publisher : GRIN Verlag
ISBN 13 : 3346177998
Total Pages : 122 pages
Book Rating : 4.3/5 (461 download)

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Book Synopsis Spline Solutions of Higher Order Boundary Value Problems by : Parcha Kalyani

Download or read book Spline Solutions of Higher Order Boundary Value Problems written by Parcha Kalyani and published by GRIN Verlag. This book was released on 2020-06-09 with total page 122 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

The Theory of Splines and Their Applications

Author : J. H. Ahlberg
Publisher : Elsevier
ISBN 13 : 1483222950
Total Pages : 297 pages
Book Rating : 4.4/5 (832 download)

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Book Synopsis The Theory of Splines and Their Applications by : J. H. Ahlberg

Download or read book The Theory of Splines and Their Applications written by J. H. Ahlberg and published by Elsevier. This book was released on 2016-06-03 with total page 297 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Boundary Value Problems From Higher Order Differential Equations

Author : Ravi P Agarwal
Publisher : World Scientific
ISBN 13 : 9814513636
Total Pages : 321 pages
Book Rating : 4.8/5 (145 download)

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Book Synopsis Boundary Value Problems From Higher Order Differential Equations by : Ravi P Agarwal

Download or read book Boundary Value Problems From Higher Order Differential Equations written by Ravi P Agarwal and published by World Scientific. This book was released on 1986-07-01 with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Spline Solutions of High-order Boundary-value Problems

Author : Shahid S. Siddiqi
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (599 download)

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Book Synopsis Spline Solutions of High-order Boundary-value Problems by : Shahid S. Siddiqi

Download or read book Spline Solutions of High-order Boundary-value Problems written by Shahid S. Siddiqi and published by . This book was released on 1994 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Higher-order numerical solutions using cubic splines

Author : S. G. Rubin
Publisher :
ISBN 13 :
Total Pages : 68 pages
Book Rating : 4.:/5 (31 download)

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Book Synopsis Higher-order numerical solutions using cubic splines by : S. G. Rubin

Download or read book Higher-order numerical solutions using cubic splines written by S. G. Rubin and published by . This book was released on 1976 with total page 68 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Splines and Variational Methods

Author : P. M. Prenter
Publisher : Courier Corporation
ISBN 13 : 0486783499
Total Pages : 338 pages
Book Rating : 4.4/5 (867 download)

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Book Synopsis Splines and Variational Methods by : P. M. Prenter

Download or read book Splines and Variational Methods written by P. M. Prenter and published by Courier Corporation. This book was released on 2013-11-26 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Numerical Solutions of Boundary Value Problems for Ordinary Differential Equations

Author : A.K. Aziz
Publisher : Academic Press
ISBN 13 : 1483267997
Total Pages : 380 pages
Book Rating : 4.4/5 (832 download)

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Book Synopsis Numerical Solutions of Boundary Value Problems for Ordinary Differential Equations by : A.K. Aziz

Download or read book Numerical Solutions of Boundary Value Problems for Ordinary Differential Equations written by A.K. Aziz and published by Academic Press. This book was released on 2014-05-10 with total page 380 pages. Available in PDF, EPUB and Kindle. Book excerpt: Numerical Solutions of Boundary Value Problems for Ordinary Differential Equations covers the proceedings of the 1974 Symposium by the same title, held at the University of Maryland, Baltimore Country Campus. This symposium aims to bring together a number of numerical analysis involved in research in both theoretical and practical aspects of this field. This text is organized into three parts encompassing 15 chapters. Part I reviews the initial and boundary value problems. Part II explores a large number of important results of both theoretical and practical nature of the field, including discussions of the smooth and local interpolant with small K-th derivative, the occurrence and solution of boundary value reaction systems, the posteriori error estimates, and boundary problem solvers for first order systems based on deferred corrections. Part III highlights the practical applications of the boundary value problems, specifically a high-order finite-difference method for the solution of two-point boundary-value problems on a uniform mesh. This book will prove useful to mathematicians, engineers, and physicists.

Application of Splines to the Numerical Solution of Two-point Boundary-value Problems

Author : Donald C. Todd
Publisher :
ISBN 13 :
Total Pages : 126 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Application of Splines to the Numerical Solution of Two-point Boundary-value Problems by : Donald C. Todd

Download or read book Application of Splines to the Numerical Solution of Two-point Boundary-value Problems written by Donald C. Todd and published by . This book was released on 1978 with total page 126 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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).

A First Course in Integral Equations

Author : Abdul-Majid Wazwaz
Publisher : World Scientific
ISBN 13 : 9789810231019
Total Pages : 228 pages
Book Rating : 4.2/5 (31 download)

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Book Synopsis A First Course in Integral Equations by : Abdul-Majid Wazwaz

Download or read book A First Course in Integral Equations written by Abdul-Majid Wazwaz and published by World Scientific. This book was released on 1997 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Data Management, Analytics and Innovation

Author : Valentina Emilia Balas
Publisher : Springer
ISBN 13 : 9811314020
Total Pages : 500 pages
Book Rating : 4.8/5 (113 download)

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Book Synopsis Data Management, Analytics and Innovation by : Valentina Emilia Balas

Download or read book Data Management, Analytics and Innovation written by Valentina Emilia Balas and published by Springer. This book was released on 2018-08-09 with total page 500 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book presents the latest, high-quality, technical contributions and research findings in the areas of data management and smart computing, big data management, artificial intelligence and data analytics, along with advances in network technologies. It discusses state-of-the-art topics as well as the challenges and solutions for future development. It includes original and previously unpublished international research work highlighting research domains from different perspectives. This book is mainly intended for researchers and practitioners in academia and industry.

Spline Collocation Approximations to Solutions of a Class of Boundary Value Problems for Partial Differential Equations which Arise in Control Theory

Download Spline Collocation Approximations to Solutions of a Class of Boundary Value Problems for Partial Differential Equations which Arise in Control Theory PDF Online Free

Author : Wayne Wilroy Wallace
Publisher :
ISBN 13 :
Total Pages : 260 pages
Book Rating : 4.:/5 (89 download)

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Book Synopsis Spline Collocation Approximations to Solutions of a Class of Boundary Value Problems for Partial Differential Equations which Arise in Control Theory by : Wayne Wilroy Wallace

Download or read book 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 published by . This book was released on 1975 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Mesh Methods

Author : Viktor A. Rukavishnikov
Publisher : MDPI
ISBN 13 : 3036503765
Total Pages : 128 pages
Book Rating : 4.0/5 (365 download)

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Book Synopsis Mesh Methods by : Viktor A. Rukavishnikov

Download or read book Mesh Methods written by Viktor A. Rukavishnikov and published by MDPI. This book was released on 2021-03-29 with total page 128 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical models of various natural processes are described by differential equations, systems of partial differential equations and integral equations. In most cases, the exact solution to such problems cannot be determined; therefore, one has to use grid methods to calculate an approximate solution using high-performance computing systems. These methods include the finite element method, the finite difference method, the finite volume method and combined methods. In this Special Issue, we bring to your attention works on theoretical studies of grid methods for approximation, stability and convergence, as well as the results of numerical experiments confirming the effectiveness of the developed methods. Of particular interest are new methods for solving boundary value problems with singularities, the complex geometry of the domain boundary and nonlinear equations. A part of the articles is devoted to the analysis of numerical methods developed for calculating mathematical models in various fields of applied science and engineering applications. As a rule, the ideas of symmetry are present in the design schemes and make the process harmonious and efficient.

Boundary Integral Equation Methods and Numerical Solutions

Author : Christian Constanda
Publisher : Springer
ISBN 13 : 3319263099
Total Pages : 242 pages
Book Rating : 4.3/5 (192 download)

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Book Synopsis Boundary Integral Equation Methods and Numerical Solutions by : Christian Constanda

Download or read book Boundary Integral Equation Methods and Numerical Solutions written by Christian Constanda and published by Springer. This book was released on 2016-03-16 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents and explains a general, efficient, and elegant method for solving the Dirichlet, Neumann, and Robin boundary value problems for the extensional deformation of a thin plate on an elastic foundation. The solutions of these problems are obtained both analytically—by means of direct and indirect boundary integral equation methods (BIEMs)—and numerically, through the application of a boundary element technique. The text discusses the methodology for constructing a BIEM, deriving all the attending mathematical properties with full rigor. The model investigated in the book can serve as a template for the study of any linear elliptic two-dimensional problem with constant coefficients. The representation of the solution in terms of single-layer and double-layer potentials is pivotal in the development of a BIEM, which, in turn, forms the basis for the second part of the book, where approximate solutions are computed with a high degree of accuracy. The book is intended for graduate students and researchers in the fields of boundary integral equation methods, computational mechanics and, more generally, scientists working in the areas of applied mathematics and engineering. Given its detailed presentation of the material, the book can also be used as a text in a specialized graduate course on the applications of the boundary element method to the numerical computation of solutions in a wide variety of problems.

Numerical Solution of Two Point Boundary Value Problems

Author : Herbert B. Keller
Publisher : SIAM
ISBN 13 : 9781611970449
Total Pages : 69 pages
Book Rating : 4.9/5 (74 download)

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Book Synopsis Numerical Solution of Two Point Boundary Value Problems by : Herbert B. Keller

Download or read book Numerical Solution of Two Point Boundary Value Problems written by Herbert B. Keller and published by SIAM. This book was released on 1976-01-01 with total page 69 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lectures on a unified theory of and practical procedures for the numerical solution of very general classes of linear and nonlinear two point boundary-value problems.

The Numerical Solution of Differential and Integral Equations by Spline Functions

Author : Hing Sum Hung
Publisher :
ISBN 13 :
Total Pages : 322 pages
Book Rating : 4.:/5 (89 download)

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Book Synopsis The Numerical Solution of Differential and Integral Equations by Spline Functions by : Hing Sum Hung

Download or read book The Numerical Solution of Differential and Integral Equations by Spline Functions written by Hing Sum Hung and published by . This book was released on 1970 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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).

Numerical Treatment of Boundary Value Problems Using Spline Functions

Author : Waheed Zahra
Publisher : LAP Lambert Academic Publishing
ISBN 13 : 9783843386647
Total Pages : 112 pages
Book Rating : 4.3/5 (866 download)

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Book Synopsis Numerical Treatment of Boundary Value Problems Using Spline Functions by : Waheed Zahra

Download or read book Numerical Treatment of Boundary Value Problems Using Spline Functions written by Waheed Zahra and published by LAP Lambert Academic Publishing. This book was released on 2010-12 with total page 112 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Quartic-spline Collocation Methods for Fourth-order Two-point Boundary Value Problems

Author : Ying Zhu
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (133 download)

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Book Synopsis Quartic-spline Collocation Methods for Fourth-order Two-point Boundary Value Problems by : Ying Zhu

Download or read book Quartic-spline Collocation Methods for Fourth-order Two-point Boundary Value Problems written by Ying Zhu and published by . This book was released on 2001 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.