About the Book
Numerical methods for ordinary di erential equations are methods used to nd
numerical approximations to the solutions of ordinary di erential equations
(ODEs). Their use is also known as "numerical integration", although this term is
sometimes taken to mean the computation of integrals. An ordinary di erential
equation or ODE is a di erential equation containing one or more functions of
one independent variable and its derivatives. The term "ordinary" is used in
contrast with the term partial di erential equation which may be with respect to
more than one independent variable. Ordinary di erential equations are ubiquitous
in science and engineering: in geometry and mechanics from the rst examples
onwards (Newton, Leibniz, Euler, Lagrange), in chemical reaction kinetics,
molecular dynamics, electronic circuits, population dynamics, and many more
application areas. They also arise, after semi discretization in space, in the
numerical treatment of time-dependent partial di erential equations, which are
even more impressively omnipresent in our technologically developed and
nancially controlled world. The book Numerical Solution of Ordinary Di erential
Equations o ers a complete and easy-to-follow introduction to classical
topics in the numerical solution of ordinary di erential equations. The book's
approach not only explains the presented mathematics, but also helps readers
understand how these numerical methods are used to solve real-world problems.