book1989

САМАРСКИЙ Александр Андреевич, ГУЛИН Алексей Владимирович

ЧИСЛЕННЫЕ МЕТОДЫ

З а в е д у ю щ и й	р е д а к ц и е й Е. Ю. Ходан
Р е д а к т о р	Т. Н. Галишникова
Х у д о ж е с т в е н н ы й	р е д а к т о р Т. Н. Кольченко
Т е х н и ч е с к и е р е д а к т о р ы		Е, В . Морозова, С. Я. Шкляр
К о р р е к т о р ы : Т. Е,		Егорова, Т. С. Вайсберг

			И Б	Мз 1 1 7 4 0
С д а н о	в	н а б о р	1 9 . 0 7 . 8 8 .	П о д п и с а н о		к	п е ч а т и		0 9 . 0 2 . 8 9 .
Ф о р м а т		6 0 X 9 0 / 1 6 .	Б у м а г а	к н и ж н о - ж у р н а л ь н а я . Г а р н и т у р а
л и т е р а т у р н а я . П е ч а т ь в ы с е к а я .					У е л .	п е ч .	л .	2 7 .	У е л . к р . -
о т т . 2 7 . У ч . - и з д . л . 2 7 , 3 1 . Т и р а ж					3 6 0 0 0 э к з .			З а к а з	№ 4 6 2 4 .
			Ц е н а 1 р . 2 0 к .

О р д е н а Т р у д о в о г о К р а с н о г о З н а м е н и и з д а т е л ь с т в о « Н а у к а » Г л а в н а я р е д а к ц и я ф и з и к о - м а т е м а т и ч е с к о й л и т е р а т у р ы

1 1 7 0 7 1 М о с к в а В - 7 1 , Л е н и н с к и й п р о с п е к т , 15

В т о р а я т и п о г р а ф и я и з д а т е л ь с т в а « Н а у к а » , 1 2 1 0 9 9 М о с к в а , Ш у б и н с к и й п е р . , 6

Alexander SAMARSKII and Alexei GOOLIN

NUMERICAL METHODS

Moskow, Nauka, Main Editorial B e d ior Physical and Mathematical Literature,

1989

Readership: Applied and computational mathematicians, college teachers and stu­ dents.

Summary: The material of this book comes from courses that the authors has ottered in the Computational Mathematics and Cybernetics Department at

Moscow State University. It consists of three parts. Part	1	is of	introduc­
tory nature. Here the idea of computational experiment as	a	tool	of scien­

tific researches is given, also some theoretical notions related to numerical methods are presented. Part 2 includes such traditional topics as interpola­

tion, numerical	integration, numerical linear and non-linear algebra, Run-
ge — Kutta and	multistep	methods for ordinary differential equations. Part
3 which based	on original	authors papers presents the theory of difference

schemes for partial differential equations including the methods of construc­ tion and investigation of difference schemes as well as direct and iteration methods for solving grid equations.

Contents:	1. Mathematical					simulation and numerical experiment. 2. Roundoff er­
rors. 3. Two-order difference equations. 4. Direct and iteration methods for
solving			systems		of	linear algebraic equations. 5. Interpolation. 6. Solving
of	nonlinear			equations. 7. Numerical integration. 8. Numerical methods for
ordinary			differential			equations. 9. The main notions of the difference sche­
mes		theory.		10.	The maximume principle and variable dividing		for diffe­
rence		schemes.			11.	Stability theory ol difference schemes. 12.	Direct and
iteration			methods for			grid equations.

The authors: Academician A. A. Samarskii is a chief of department of Keldysh Institute of Applied Mathematics, Academy of Science of the USSR, the chairman of the Scientific Council on the problem «Mathematical modelling» Academy of Science of the USSR, the Hero of Socialist Labour, the Lenin and State Prises winner. He is the author of number monographs and text­ books on mathematical physics, theory of difference schemes and numerical methods such as follows.

The equations of mathematical physics (together with A. N. Tichonov), trans­ lated into English, German, French. Theory of difference schemes, translated into

English.	Stability	of	difference	schemes	(together	with A.		V. Goolin). Difference
schemes	for elliptic		equations	(together	with V.	B.	Andreev),		translated	into
French.	difference	methods for		gas dynamic problems			(together		with Yu. P. Po-
The
pov).
Numerical methods for grid equations (together with								E. S. Nikolaev),		trans­
lated into English,		French, Italian. D. s. A. V. Goolin					is a	professor of Computa­

tional Mathematics and Cybernetics Department at Moscow State University, a specialist in the field of numerical methods for differential equations.