Numerical Initial Value Problems in Ordinary Differential Equations

Fülszöveg

Professor Gear treats all classes of
step-by-step methods suitable to auto-
matic integration of general problems.
No previous knowledge of computer
programming is required, and the
book is organized so that complex
mathematical theory can be omitted.
Among the contents are chapters deal-
ing with Euler method; higher order
one-step methods; systems of equa-
tions and equations of order greater
than one; convergence, error bounds
and error estimates for one-step meth-
ods; the choice of step size and order;
extrapolation methods; an introduc-
tion to multivalue and multistep meth-
ods; general multistep methods, order
and stability; multivalue methods;
existence, convergence and error esti-
mates for multivalue methods; special
methods for special problems; and
choosing a method.
AMONG THE FEATURES
• Broad coverage includes methods
for Stiff equations, multistep meth-
ods, convergence and error theory
of predictor corrector methods, and
extrapolation... Tovább

Fülszöveg

Professor Gear treats all classes of
step-by-step methods suitable to auto-
matic integration of general problems.
No previous knowledge of computer
programming is required, and the
book is organized so that complex
mathematical theory can be omitted.
Among the contents are chapters deal-
ing with Euler method; higher order
one-step methods; systems of equa-
tions and equations of order greater
than one; convergence, error bounds
and error estimates for one-step meth-
ods; the choice of step size and order;
extrapolation methods; an introduc-
tion to multivalue and multistep meth-
ods; general multistep methods, order
and stability; multivalue methods;
existence, convergence and error esti-
mates for multivalue methods; special
methods for special problems; and
choosing a method.
AMONG THE FEATURES
• Broad coverage includes methods
for Stiff equations, multistep meth-
ods, convergence and error theory
of predictor corrector methods, and
extrapolation techniques.
• Provides complete FORTRAN sub-
routines for Runge-Kutta, extrapola-
tion and multistep methods — both
for general and Stiff problems.
(continued on back flap)
(continued from front flap)
• Offers both theoretical and compu-
tational problems at the end of each
chapter.
• Presents many numerical examples
of error behavior, instability effects,
and round-off effects.
• Compares different methods numer-
ically.
• Derives algorithms for controlling
the step size and order of the
method.
THE AUTHOR
C. William Gear is Professor of
Computer Science and Applied Mathe-
matics at the University of Illinois at
Urbana-Champaign. This is his sec-
ond published work. His first, pub-
lished in 1969, dealt with computers
and programming techniques. Vissza