Books in Ordinary differential equations

Singularities & Dynamical Systems

1st Edition
Volume 103
January 1, 1985
S.N. Pnevmatikos
English
eBook
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This volume is an account of the lectures delivered at the international Conference ``Singularities and Dynamical Systems-83''. The main purpose of the Conference was to create conditions of scientific contact between mathematicians and physicists who have singularities and dynamical systems as common interests.

Coupled Nonlinear Oscillators

1st Edition
Volume .
January 1, 1983
J. Chandra + 1 more
English
eBook
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Stochastic Differential Equations and Diffusion Processes

1st Edition
Volume 24
January 1, 1981
S. Watanabe + 1 more
English
Hardback
9 7 8 0 4 4 4 8 6 1 7 2 6
eBook
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Asymptotic Analysis of Singular Perturbations

1st Edition
Volume 9
August 30, 2011
W. Eckhaus
English
eBook
9 7 8 0 0 8 0 8 7 5 3 0 9

Transmutation and Operator Differential Equations

1st Edition
Volume 37
January 1, 1979
R.W. Carroll
English
eBook
9 7 8 0 0 8 0 8 7 1 4 8 6

Nonlinear Equations in Abstract Spaces

1st Edition
May 27, 2014
V. Lakshmikantham
English
eBook
9 7 8 1 4 8 3 2 7 2 1 0 8

Many problems in partial differential equations which arise from physical models can be considered as ordinary differential equations in appropriate infinite dimensional spaces, for which elegant theories and powerful techniques have recently been developed. This book gives a detailed account of the current state of the theory of nonlinear differential equations in a Banach space, and discusses existence theory for differential equations with continuous and discontinuous right-hand sides. Of special importance is the first systematic presentation of the very important and complex theory of multivalued discontinuous differential equations.

Numerical Methods for Differential Systems

1st Edition
May 12, 2014
L. Lapidus + 1 more
English
eBook
9 7 8 1 4 8 3 2 6 9 8 5 6

Numerical Methods for Differential Systems: Recent Developments in Algorithms, Software, and Applications reviews developments in algorithms, software, and applications of numerical methods for differential systems. Topics covered include numerical algorithms for ordinary and partial differential equations (ODE/PDEs); theoretical approaches to the solution of nonlinear algebraic and boundary value problems via associated differential systems; integration algorithms for initial-value ODEs with particular emphasis on stiff systems; finite difference algorithms; and general- and special-purpose computer codes for ODE/PDEs. Comprised of 15 chapters, this book begins with an introduction to high-order A-stable averaging algorithms for stiff differential systems, followed by a discussion on second derivative multistep formulas based on g-splines; numerical integration of linearized stiff ODEs; and numerical solution of large systems of stiff ODEs in a modular simulation framework. Subsequent chapters focus on numerical methods for mass action kinetics; a systematized collection of codes for solving two-point boundary value problems; general software for PDEs; and the choice of algorithms in automated method of lines solution of PDEs. The final chapter is devoted to quality software for ODEs. This monograph should be of interest to mathematicians, chemists, and chemical engineers.

Differential Equations, Dynamical Systems, and Linear Algebra

1st Edition
June 28, 1974
Morris W. Hirsch + 2 more
English
eBook
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This book is about dynamical aspects of ordinary differential equations and the relations between dynamical systems and certain fields outside pure mathematics. A prominent role is played by the structure theory of linear operators on finite-dimensional vector spaces; the authors have included a self-contained treatment of that subject.

Comparison and Oscillation Theory of Linear Differential Equations

1st Edition
June 3, 2016
C. A. Swanson
Richard Bellman
English
eBook
9 7 8 1 4 8 3 2 6 6 6 7 1

Mathematics in Science and Engineering, Volume 48: Comparison and Oscillation Theory of Linear Differential Equations deals primarily with the zeros of solutions of linear differential equations. This volume contains five chapters. Chapter 1 focuses on comparison theorems for second order equations, while Chapter 2 treats oscillation and nonoscillation theorems for second order equations. Separation, comparison, and oscillation theorems for fourth order equations are covered in Chapter 3. In Chapter 4, ordinary equations and systems of differential equations are reviewed. The last chapter discusses the result of the first analog of a Sturm-type comparison theorem for an elliptic partial differential equation. This publication is intended for college seniors or beginning graduate students who are well-acquainted with advanced calculus, complex analysis, linear algebra, and linear differential equations.

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