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Donald Greenspan
Numerical Solution of Ordinary
Differential Equations
IX
Preface
The study and application of ordinary differential equations has been a major
part of the history of mathematics. In recent years, new applications in such
areas as molecular mechanics and nanophysics have simply added to their
significance.
This book is intended to be used as either a handbook or a text for a one-
semester, introductory course in the numerical solution of ordinary differen-
tial equations. Theory, methodology, intuition, and applications are interwo-
ven throughout. The choice of methods is guided by applied, rather than
theoretical, interests. Throughout, nonlinearity and determinism are empha-
sized.
Chapter 1 develops Euler’s method and fundamental convergence theory.
Chapter 2 develops Runge–Kutta formulas through the highest order avail-
able, that is, order 10. Chapter 3 develops Taylor expansion methodology of
arbitrary orders. Chapter 4 develops conservative numerical methodology.
Chapter 5 is concerned with very large systems of differential equations, such
as those used in molecular mechanics. Chapter 6 studies practical aspects of
instability. Chapters 7 and 8 are concerned with boundary value problems.
Chapter 9 presents, in an entirely self-contained fashion, fundamentals of spe-
cial relativistic dynamics, in which the differential equations and the related
constraints are truly unique. Chapter 10 is a survey with references of the
many other topics available in the literature.
Flexibility is incorporated by providing programs generically. Computer
technology is in such a rapid state of growth that the use of a specific pro-
gramming language can e outdated in a very short time. In addition,
the individual who wishes to use a graphics routine is free to use whichever
is most readily available to him or her.
Relatively difficult sections are marked with an asterisk and m