On integration of quasilinear parabolic equations by explicit difference methods
Author:
J. Wolfgang Smith
Journal:
Trans. Amer. Math. Soc. 91 (1959), 425443
MSC:
Primary 65.68
MathSciNet review:
0141235
Fulltext PDF Free Access
References 
Similar Articles 
Additional Information
 [1]
R.
Courant, K.
Friedrichs, and H.
Lewy, Über die partiellen Differenzengleichungen der
mathematischen Physik, Math. Ann. 100 (1928),
no. 1, 32–74 (German). MR
1512478, http://dx.doi.org/10.1007/BF01448839
 [2]
Jim
Douglas Jr., On the relation between stability and convergence in
the numerical solution of linear parabolic and hyperbolic differential
equations, J. Soc. Indust. Appl. Math. 4 (1956),
20–37. MR
0080368 (18,236d)
 [3]
Jim
Douglas Jr., On the numerical integration of quasilinear parabolic
differential equations, Pacific J. Math. 6 (1956),
35–42. MR
0079196 (18,46g)
 [4]
K.
O. Friedrichs, Symmetric hyperbolic linear differential
equations, Comm. Pure Appl. Math. 7 (1954),
345–392. MR 0062932
(16,44c)
 [5]
Fritz
John, On integration of parabolic equations by difference methods.
I. Linear and quasilinear equations for the infinite interval, Comm.
Pure Appl. Math. 5 (1952), 155–211. MR 0047885
(13,947b)
 [6]
P. Lax, Difference approximation to solutions of linear differential equationsan operator theoretical approach, Lecture Series Symposium on Partial Differential Equations, University of Kansas, 1957.
 [7]
P.
D. Lax and R.
D. Richtmyer, Survey of the stability of linear finite difference
equations, Comm. Pure Appl. Math. 9 (1956),
267–293. MR 0079204
(18,48c)
 [8]
George
G. O’Brien, Morton
A. Hyman, and Sidney
Kaplan, A study of the numerical solution of partial differential
equations, J. Math. Physics 29 (1951), 223–251.
MR
0040805 (12,751e)
 [9]
Milton
E. Rose, On the integration of nonlinear parabolic equations by
implicit difference methods, Quart. Appl. Math. 14
(1956), 237–248. MR 0085610
(19,65f)
 [1]
 R. Courant, K. O. Friedrichs, and H. Lewy, Über die partiellen Differenzengleichungen der mathematischen Physik, Math. Ann. vol. 100 (1928) pp. 243255. MR 1512478
 [2]
 J. Douglas, Jr., On the relation between stability and convergence in the numerical solution of linear hyperbolic and parabolic differential equations, J. Soc. Indust. Appl. Math. vol. 4 (1956) pp. 2037. MR 0080368 (18:236d)
 [3]
 , On the numerical integration of quasilinear parabolic differential equations, Pacific J. Math. vol. 6 (1956) pp. 3542. MR 0079196 (18:46g)
 [4]
 K. O. Friedrichs, Symmetric hyperbolic linear differential equations, Comm. Pure Appl. Math. vol. 7 (1954) pp. 345392. MR 0062932 (16:44c)
 [5]
 F. John, On integration of parabolic equations by difference methods, Comm. Pure Appl. Math. vol. 5 (1952) pp. 155211. MR 0047885 (13:947b)
 [6]
 P. Lax, Difference approximation to solutions of linear differential equationsan operator theoretical approach, Lecture Series Symposium on Partial Differential Equations, University of Kansas, 1957.
 [7]
 P. Lax, and R. D. Richtmyer, Survey of the stability of linear finite difference equations, Comm. Pure Appl. Math. vol. 9 (1956) pp. 267293. MR 0079204 (18:48c)
 [8]
 G. G. O'Brien, M. A. Hyman and S. Kaplan, A study of the numerical solution of partial differential equations, J. Math. Phys. vol. 29 (1951) pp. 223251. MR 0040805 (12:751e)
 [9]
 M. E. Rose, On the integration of nonlinear parabolic equations by implicit difference methods, Quart. Appl. Math. vol. 14 (1956) pp. 237248. MR 0085610 (19:65f)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029947195901412356
PII:
S 00029947(1959)01412356
Article copyright:
© Copyright 1959
American Mathematical Society
