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This new work is an introduction to the numerical solution of the
initial value problem for a system of ordinary differential
equations. The first three chapters are general in nature, and
chapters 4 through 8 derive the basic numerical methods, prove
their convergence, study their stability and consider how to
implement them effectively. The book focuses on the most important
methods in practice and develops them fully, uses examples
throughout, and emphasizes practical problem-solving methods.
This new work is an introduction to the numerical solution of the
initial value problem for a system of ordinary differential
equations. The first three chapters are general in nature, and
chapters 4 through 8 derive the basic numerical methods, prove
their convergence, study their stability and consider how to
implement them effectively. The book focuses on the most important
methods in practice and develops them fully, uses examples
throughout, and emphasizes practical problem-solving methods.
This book is a text for a one-semester course for upper-level undergraduates and beginning graduate students in engineering, science, and mathematics. Prerequisites are a first course in the theory of ODEs and a survey course in numerical analysis, in addition to specific programming experience, preferably in MATLAB, and knowledge of elementary matrix theory. Professionals will also find that this useful concise reference contains reviews of technical issues and realistic and detailed examples. The programs for the examples are supplied on the accompanying web site and can serve as templates for solving other problems. Each chapter begins with a discussion of the "facts of life" for the problem, mainly by means of examples. Numerical methods for the problem are then developed, but only those methods most widely used. The treatment of each method is brief and technical issues are minimized, but all the issues important in practice and for understaning the codes are discussed. The last part of each chapter is a tutorial that shows how to solve problems by means of small, but realistic, examples.
This book examines the solution of some of the most common problems
of numerical computation. By concentrating on one effective
algorithm for each basic task, it develops the fundamental theory
in a brief, elementary way. There are ample exercises, and codes
are provided to reduce the time otherwise required for programming
and debugging. Exposes readers to art of numerical computing as
well as the science. Readers need only a familiarity with either
FORTRAN or C. Applications are taken from a variety of disciplines
including engineering, physics, and chemistry.
This book is a text for a one-semester course for upper-level undergraduates and beginning graduate students in engineering, science, and mathematics. Prerequisites are a first course in the theory of ODEs and a survey course in numerical analysis, in addition to specific programming experience, preferably in MATLAB, and knowledge of elementary matrix theory. Professionals will also find that this useful concise reference contains reviews of technical issues and realistic and detailed examples. The programs for the examples are supplied on the accompanying web site and can serve as templates for solving other problems. Each chapter begins with a discussion of the "facts of life" for the problem, mainly by means of examples. Numerical methods for the problem are then developed, but only those methods most widely used. The treatment of each method is brief and technical issues are minimized, but all the issues important in practice and for understaning the codes are discussed. The last part of each chapter is a tutorial that shows how to solve problems by means of small, but realistic, examples.
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