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Название: Numerical Methods for Differential Equations and Applications
Автор: Liviu Gr. Ixaru
Издательство: D. Reidel Publishing Company - Kluwer Academic Publishers
Размер: 19,7 МБ
This book concerns numerical analysis and, more particularly, the numerical analysis needed to deal with the ordinary differential equations one meets in quantum physics, chemistry and engineering. The book was especially written with such potential active users of numerical methods in mind.
This book is merely addressed to persons who, without being profes¬sionals in applied mathematics, are often faced with the problem of numerically solving differential equations.
Graduate students and persons who are active in the research in theoretical physics, chemistry or engineering are perhaps the most suited readers.
In writing this book, special attention was paid to keep some balance between rigour and accessibility. Thus, use is made of only a background level of knowledge in mathematics which is typically achieved during training in the faculties of physics, chemistry and technical branches. At the same time, although the presentation is generally rigorous, on some occasions we deliberately sacrificed rigour in favour of accessibility.
The presentation of various methods includes all aspects of interest: theory — which is necessary for those who are rather deeply engaged in the field — , algorithms and programming advices — for hurried readers. The book also contains a lot of numerical examples treated up to the very end, sometimes just with programs included.
The book is organized into five chapters. In each of the first three chapters a definite class of methods is discussed for the solution of the initial value problem for ordinary differential equations. It should be mentioned that, while the first two classes, that is of multistep and of one-step methods, are largely presented in the literature, we also consider a new class of methods (the so-called piecewise perturbation methods) which was developed only recently. As a matter of fact, it is now the first time, to our knowledge, that such methods are treated in a self¬standing chapter of a book of numerical methods.
The fourth chapter is mainly focussed on the boundary value problems for linear second-order equations. A special section is here devoted to the Schrodinger equation, the basic equation of quantum mechanics.
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