Boundary Value Problems From Higher Order Differential Equations
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| Author | : Ravi P Agarwal |
| Publisher | : World Scientific |
| Total Pages | : 321 |
| Release | : 1986-07-01 |
| Genre | : Mathematics |
| ISBN | : 9814513636 |
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 | : William F. Trench |
| Publisher | : Thomson Brooks/Cole |
| Total Pages | : 764 |
| Release | : 2001 |
| Genre | : Mathematics |
| ISBN | : |
Written in a clear and accurate language that students can understand, Trench's new book minimizes the number of explicitly stated theorems and definitions. Instead, he deals with concepts in a conversational style that engages students. He includes more than 250 illustrated, worked examples for easy reading and comprehension. One of the book's many strengths is its problems, which are of consistently high quality. Trench includes a thorough treatment of boundary-value problems and partial differential equations and has organized the book to allow instructors to select the level of technology desired. This has been simplified by using symbols, C and L, to designate the level of technology. C problems call for computations and/or graphics, while L problems are laboratory exercises that require extensive use of technology. Informal advice on the use of technology is included in several sections and instructors who prefer not to emphasize technology can ignore these exercises without interrupting the flow of material.
| Author | : Filippo Gazzola |
| Publisher | : Springer |
| Total Pages | : 444 |
| Release | : 2010-05-26 |
| Genre | : Mathematics |
| ISBN | : 3642122450 |
This accessible monograph covers higher order linear and nonlinear elliptic boundary value problems in bounded domains, mainly with the biharmonic or poly-harmonic operator as leading principal part. It provides rapid access to recent results and references.
| Author | : Johnny Henderson |
| Publisher | : Academic Press |
| Total Pages | : 323 |
| Release | : 2015-10-30 |
| Genre | : Mathematics |
| ISBN | : 0128036796 |
Boundary Value Problems for Systems of Differential, Difference and Fractional Equations: Positive Solutions discusses the concept of a differential equation that brings together a set of additional constraints called the boundary conditions. As boundary value problems arise in several branches of math given the fact that any physical differential equation will have them, this book will provide a timely presentation on the topic. Problems involving the wave equation, such as the determination of normal modes, are often stated as boundary value problems. To be useful in applications, a boundary value problem should be well posed. This means that given the input to the problem there exists a unique solution, which depends continuously on the input. Much theoretical work in the field of partial differential equations is devoted to proving that boundary value problems arising from scientific and engineering applications are in fact well-posed. - Explains the systems of second order and higher orders differential equations with integral and multi-point boundary conditions - Discusses second order difference equations with multi-point boundary conditions - Introduces Riemann-Liouville fractional differential equations with uncoupled and coupled integral boundary conditions
| Author | : R.P. Agarwal |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 302 |
| Release | : 2013-03-09 |
| Genre | : Mathematics |
| ISBN | : 9401715688 |
The last fifty years have witnessed several monographs and hundreds of research articles on the theory, constructive methods and wide spectrum of applications of boundary value problems for ordinary differential equations. In this vast field of research, the conjugate (Hermite) and the right focal point (Abei) types of problems have received the maximum attention. This is largely due to the fact that these types of problems are basic, in the sense that the methods employed in their study are easily extendable to other types of prob lems. Moreover, the conjugate and the right focal point types of boundary value problems occur frequently in real world problems. In the monograph Boundary Value Problems for Higher Order Differential Equations published in 1986, we addressed the theory of conjugate boundary value problems. At that time the results on right focal point problems were scarce; however, in the last ten years extensive research has been done. In Chapter 1 of the mono graph we offer up-to-date information of this newly developed theory of right focal point boundary value problems. Until twenty years ago Difference Equations were considered as the dis cretizations of the differential equations. Further, it was tacitly taken for granted that the theories of difference and differential equations are parallel. However, striking diversities and wide applications reported in the last two decades have made difference equations one of the major areas of research.
| Author | : Dr Jitendra Singh |
| Publisher | : Dr. Jitendra Singh |
| Total Pages | : 157 |
| Release | : 2024-10-02 |
| Genre | : Mathematics |
| ISBN | : |
This book, "Advanced Ordinary Differential Equations and Boundary Value Problems," is designed for students preparing for the CSIR NET (JRF) Mathematical Science exam and other competitive mathematics exams. It provides a comprehensive exploration of essential topics in advanced differential equations. Chapter 1 delves into Sturm-Liouville Theory, focusing on eigenvalue problems, the orthogonality of eigenfunctions, and various applications, which are crucial for understanding the behavior of differential operators and their solutions. Chapter 2 introduces Green's Functions for Ordinary Differential Equations (ODEs). It covers the construction and application of Green’s functions to boundary value problems, offering a robust technique for solving differential equations with specific boundary conditions. Chapter 3 addresses Higher-Order Linear ODEs, presenting the general theory and solution methods for these equations. It also explores their applications in physics and engineering, demonstrating their relevance to practical problems. This book aims to equip readers with the theoretical foundation and problem-solving skills necessary for tackling advanced topics in differential equations and boundary value problems.
| Author | : Irena Rachůnková |
| Publisher | : Springer |
| Total Pages | : 194 |
| Release | : 2015-09-29 |
| Genre | : Mathematics |
| ISBN | : 9462391270 |
This book offers the reader a new approach to the solvability of boundary value problems with state-dependent impulses and provides recently obtained existence results for state dependent impulsive problems with general linear boundary conditions. It covers fixed-time impulsive boundary value problems both regular and singular and deals with higher order differential equations or with systems that are subject to general linear boundary conditions. We treat state-dependent impulsive boundary value problems, including a new approach giving effective conditions for the solvability of the Dirichlet problem with one state-dependent impulse condition and we show that the depicted approach can be extended to problems with a finite number of state-dependent impulses. We investigate the Sturm–Liouville boundary value problem for a more general right-hand side of a differential equation. Finally, we offer generalizations to higher order differential equations or differential systems subject to general linear boundary conditions.
| Author | : Dennis G. Zill |
| Publisher | : |
| Total Pages | : 619 |
| Release | : 2005 |
| Genre | : Boundary value problems |
| ISBN | : 9780534420741 |
Now enhanced with the innovative DE Tools CD-ROM and the iLrn teaching and learning system, this proven text explains the "how" behind the material and strikes a balance between the analytical, qualitative, and quantitative approaches to the study of differential equations. This accessible text speaks to students through a wealth of pedagogical aids, including an abundance of examples, explanations, "Remarks" boxes, definitions, and group projects. This book was written with the student's understanding firmly in mind. Using a straightforward, readable, and helpful style, this book provides a thorough treatment of boundary-value problems and partial differential equations.
| Author | : Vladimir Dobrushkin |
| Publisher | : CRC Press |
| Total Pages | : 1225 |
| Release | : 2017-10-19 |
| Genre | : Mathematics |
| ISBN | : 1498733727 |
Applied Differential Equations with Boundary Value Problems presents a contemporary treatment of ordinary differential equations (ODEs) and an introduction to partial differential equations (PDEs), including their applications in engineering and the sciences. This new edition of the author’s popular textbook adds coverage of boundary value problems. The text covers traditional material, along with novel approaches to mathematical modeling that harness the capabilities of numerical algorithms and popular computer software packages. It contains practical techniques for solving the equations as well as corresponding codes for numerical solvers. Many examples and exercises help students master effective solution techniques, including reliable numerical approximations. This book describes differential equations in the context of applications and presents the main techniques needed for modeling and systems analysis. It teaches students how to formulate a mathematical model, solve differential equations analytically and numerically, analyze them qualitatively, and interpret the results.
| Author | : Parcha Kalyani |
| Publisher | : GRIN Verlag |
| Total Pages | : 122 |
| Release | : 2020-06-09 |
| Genre | : Mathematics |
| ISBN | : 3346177998 |
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.
