Spline Solutions Of Higher Order Boundary Value Problems

Author : Parcha Kalyani
Publisher : GRIN Verlag
Page : 122 pages
File Size : 44,7 Mb
Release : 2020-06-09
Category : Mathematics
ISBN : 9783346177995

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Spline Solutions of Higher Order Boundary Value Problems by Parcha Kalyani Pdf

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.

Author : S. G. Rubin,P. K. Khosla
Publisher : Unknown
Page : 68 pages
File Size : 40,7 Mb
Release : 1976
Category : Differential equations, Partial
ISBN : NASA:31769000498264

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Higher-order Numerical Solutions Using Cubic Splines by S. G. Rubin,P. K. Khosla Pdf

Author : P. M. Prenter
Publisher : Courier Corporation
Page : 338 pages
File Size : 47,7 Mb
Release : 2013-11-26
Category : Mathematics
ISBN : 9780486783499

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Splines and Variational Methods by P. M. Prenter Pdf

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 : Ali Ümit Keskin
Publisher : Springer
Page : 517 pages
File Size : 49,7 Mb
Release : 2019-06-19
Category : Technology & Engineering
ISBN : 9783030210809

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Boundary Value Problems for Engineers by Ali Ümit Keskin Pdf

This book is designed to supplement standard texts and teaching material in the areas of differential equations in engineering such as in Electrical ,Mechanical and Biomedical engineering. Emphasis is placed on the Boundary Value Problems that are often met in these fields.This keeps the the spectrum of the book rather focussed .The book has basically emerged from the need in the authors lectures on “Advanced Numerical Methods in Biomedical Engineering” at Yeditepe University and it is aimed to assist the students in solving general and application specific problems in Science and Engineering at upper-undergraduate and graduate level.Majority of the problems given in this book are self-contained and have varying levels of difficulty to encourage the student. Problems that deal with MATLAB simulations are particularly intended to guide the student to understand the nature and demystify theoretical aspects of these problems. Relevant references are included at the end of each chapter. Here one will also find large number of software that supplements this book in the form of MATLAB script (.m files). The name of the files used for the solution of a problem are indicated at the end of each corresponding problem statement.There are also some exercises left to students as homework assignments in the book. An outstanding feature of the book is the large number and variety of the solved problems that are included in it. Some of these problems can be found relatively simple, while others are more challenging and used for research projects. All solutions to the problems and script files included in the book have been tested using recent MATLAB software.The features and the content of this book will be most useful to the students studying in Engineering fields, at different levels of their education (upper undergraduate-graduate).

Author : Ravi P Agarwal
Publisher : World Scientific
Page : 321 pages
File Size : 46,5 Mb
Release : 1986-07-01
Category : Mathematics
ISBN : 9789814513630

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Boundary Value Problems From Higher Order Differential Equations by Ravi P Agarwal Pdf

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

Author : J. H. Ahlberg,E. N. Nilson,J. L. Walsh
Publisher : Elsevier
Page : 296 pages
File Size : 47,6 Mb
Release : 2016-06-03
Category : Mathematics
ISBN : 9781483222950

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The Theory of Splines and Their Applications by J. H. Ahlberg,E. N. Nilson,J. L. Walsh Pdf

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 : Jagdev Singh,George A. Anastassiou,Dumitru Baleanu,Devendra Kumar
Publisher : Springer Nature
Page : 589 pages
File Size : 55,9 Mb
Release : 2023-04-12
Category : Technology & Engineering
ISBN : 9783031299599

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Advances in Mathematical Modelling, Applied Analysis and Computation by Jagdev Singh,George A. Anastassiou,Dumitru Baleanu,Devendra Kumar Pdf

The book is very useful for researchers, graduate students and educators associated with or interested in recent advances in different aspects of modelling, computational methods and techniques necessary for solving problems arising in the real-world problems. The book includes carefully peer-reviewed research articles presented in the “5th International Conference on Mathematical Modelling, Applied Analysis and Computation”, held at JECRC University, Jaipur, during 4–6 August 2022 concentrating on current advances in mathematical modelling and computation via tools and techniques from mathematics and allied areas. It is focused on papers dealing with necessary theory and methods in a balanced manner and contributes towards solving problems arising in engineering, control systems, networking system, environment science, health science, physical and biological systems, social issues of current interest, etc.

Author : Dumitru Baleanu
Publisher : MDPI
Page : 348 pages
File Size : 51,9 Mb
Release : 2021-01-20
Category : Computers
ISBN : 9783039368709

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Advances in Differential and Difference Equations with Applications 2020 by Dumitru Baleanu Pdf

It is very well known that differential equations are related with the rise of physical science in the last several decades and they are used successfully for models of real-world problems in a variety of fields from several disciplines. Additionally, difference equations represent the discrete analogues of differential equations. These types of equations started to be used intensively during the last several years for their multiple applications, particularly in complex chaotic behavior. A certain class of differential and related difference equations is represented by their respective fractional forms, which have been utilized to better describe non-local phenomena appearing in all branches of science and engineering. The purpose of this book is to present some common results given by mathematicians together with physicists, engineers, as well as other scientists, for whom differential and difference equations are valuable research tools. The reported results can be used by researchers and academics working in both pure and applied differential equations.

Author : Samsul Ariffin Abdul Karim,Afza Shafie
Publisher : Springer Nature
Page : 439 pages
File Size : 55,6 Mb
Release : 2021-09-17
Category : Technology & Engineering
ISBN : 9783030796068

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Towards Intelligent Systems Modeling and Simulation by Samsul Ariffin Abdul Karim,Afza Shafie Pdf

This book creates the emergence of disruptive technologies that have led to a significant change in the role of mathematics and statistics for problem solving, with the use of sophisticated software and hardware in solving complex systems and process. In the era of digital technology, mathematics and statistics need to be highly relevant to be able to cater for the needs of IR4.0 such as big data analytics, simulation, autonomous system, and cloud computing. Motivated by this development, a total of 26 chapters are contributed by respectable experts for this book. The main scope of the book is to conduct a new system of modeling and simulations on solving differential equations, nonlinear equations, energy, epidemiology, and risk assessment. This book is of interest for postgraduate students, researchers as well as other scientists who are working in numerical modeling and simulations based on efficient mathematical and statistical techniques.

Author : D. Srinivasacharya,K. Srinivas Reddy
Publisher : Springer
Page : 657 pages
File Size : 52,6 Mb
Release : 2018-12-13
Category : Technology & Engineering
ISBN : 9789811319037

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Numerical Heat Transfer and Fluid Flow by D. Srinivasacharya,K. Srinivas Reddy Pdf

This book comprises selected papers from the International Conference on Numerical Heat Transfer and Fluid Flow (NHTFF 2018), and presents the latest developments in computational methods in heat and mass transfer. It also discusses numerical methods such as finite element, finite difference, and finite volume applied to fluid flow problems. Providing a good balance between computational methods and analytical results applied to a wide variety of problems in heat transfer, transport and fluid mechanics, the book is a valuable resource for students and researchers working in the field of heat transfer and fluid dynamics.

Author : Sio-Iong Ao,Len Gelman,Haeng Kon Kim
Publisher : Springer
Page : 407 pages
File Size : 47,5 Mb
Release : 2018-08-17
Category : Technology & Engineering
ISBN : 9789811307461

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Transactions on Engineering Technologies by Sio-Iong Ao,Len Gelman,Haeng Kon Kim Pdf

This volume contains a selection of revised and extended research articles written by prominent researchers participating in a large international conference on Advances in Engineering Technologies and Physical Science which was held in London, UK, 5-7 July, 2017. Topics covered include mechanical engineering, engineering mathematics, computer science, knowledge engineering, electrical engineering, wireless networks, and industrial applications. With contributions carefully chosen to represent the most cutting-edge research presented during the conference, the book offers the state of art in engineering technologies and physical science and applications, and also serves as an excellent reference work for researchers and graduate students working with/on engineering technologies and physical science and applications.

Author : Abdul-Majid Wazwaz
Publisher : World Scientific
Page : 228 pages
File Size : 48,5 Mb
Release : 1997
Category : Mathematics
ISBN : 9810231016

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A First Course in Integral Equations by Abdul-Majid Wazwaz Pdf

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.

Author : Jagdev Singh,Devendra Kumar,Hemen Dutta,Dumitru Baleanu,Sunil Dutt Purohit
Publisher : Springer Nature
Page : 311 pages
File Size : 42,9 Mb
Release : 2019-08-31
Category : Mathematics
ISBN : 9789811396083

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Mathematical Modelling, Applied Analysis and Computation by Jagdev Singh,Devendra Kumar,Hemen Dutta,Dumitru Baleanu,Sunil Dutt Purohit Pdf

This book contains original research papers presented at the International Conference on Mathematical Modelling, Applied Analysis and Computation, held at JECRC University, Jaipur, India, on 6-8 July, 2018. Organized into 20 chapters, the book focuses on theoretical and applied aspects of various types of mathematical modelling such as equations of various types, fuzzy mathematical models, automata, Petri nets and bond graphs for systems of dynamic nature and the usage of numerical techniques in handling modern problems of science, engineering and finance. It covers the applications of mathematical modelling in physics, chemistry, biology, mechanical engineering, civil engineering, computer science, social science and finance. A wide variety of dynamical systems like deterministic, stochastic, continuous, discrete or hybrid, with respect to time, are discussed in the book. It provides the mathematical modelling of various problems arising in science and engineering, and also new efficient numerical approaches for solving linear and nonlinear problems and rigorous mathematical theories, which can be used to analyze a different kind of mathematical models. The conference was aimed at fostering cooperation among students and researchers in areas of applied analysis, engineering and computation with the deliberations to inculcate new research ideas in their relevant fields. This volume will provide a comprehensive introduction to recent theories and applications of mathematical modelling and numerical simulation, which will be a valuable resource for graduate students and researchers of mathematical modelling and industrial mathematics.

Author : Steve Baigent,Martin Bohner,Saber Elaydi
Publisher : Springer Nature
Page : 440 pages
File Size : 42,8 Mb
Release : 2021-01-04
Category : Mathematics
ISBN : 9783030601072

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Progress on Difference Equations and Discrete Dynamical Systems by Steve Baigent,Martin Bohner,Saber Elaydi Pdf

This book comprises selected papers of the 25th International Conference on Difference Equations and Applications, ICDEA 2019, held at UCL, London, UK, in June 2019. The volume details the latest research on difference equations and discrete dynamical systems, and their application to areas such as biology, economics, and the social sciences. Some chapters have a tutorial style and cover the history and more recent developments for a particular topic, such as chaos, bifurcation theory, monotone dynamics, and global stability. Other chapters cover the latest personal research contributions of the author(s) in their particular area of expertise and range from the more technical articles on abstract systems to those that discuss the application of difference equations to real-world problems. The book is of interest to both Ph.D. students and researchers alike who wish to keep abreast of the latest developments in difference equations and discrete dynamical systems.

Author : Larry L. Schumaker
Publisher : SIAM
Page : 413 pages
File Size : 45,7 Mb
Release : 2015-01-01
Category : Science
ISBN : 9781611973907

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Spline Functions by Larry L. Schumaker Pdf

This book describes in detail the key algorithms needed for computing with spline functions and illustrates their use in solving several basic problems in numerical analysis, including function approximation, numerical quadrature, data fitting, and the numerical solution of PDE's. The focus is on computational methods for bivariate splines on triangulations in the plane and on the sphere, although both univariate and tensor-product splines are also discussed. The book contains numerous examples and figures to illustrate the methods and their performance. All of the algorithms in the book have been coded in a separate MATLAB package available for license. The package can be used to run all of the examples in the book and also provides readers with the essential tools needed to create software for their own applications. In addition to the included bibliography, a list of over 100 pages of additional references can be found on the book's website.