On integration of quasi-linear parabolic equations by explicit difference methods

Author:
J. Wolfgang Smith

Journal:
Trans. Amer. Math. Soc. **91** (1959), 425-443

MSC:
Primary 65.68

MathSciNet review:
0141235

Full-text 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**, 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****[3]**Jim Douglas Jr.,*On the numerical integration of quasilinear parabolic differential equations*, Pacific J. Math.**6**(1956), 35–42. MR**0079196****[4]**K. O. Friedrichs,*Symmetric hyperbolic linear differential equations*, Comm. Pure Appl. Math.**7**(1954), 345–392. MR**0062932****[5]**Fritz John,*On integration of parabolic equations by difference methods. I. Linear and quasi-linear equations for the infinite interval*, Comm. Pure Appl. Math.**5**(1952), 155–211. MR**0047885****[6]**P. Lax,*Difference approximation to solutions of linear differential equations--an 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****[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****[9]**Milton E. Rose,*On the integration of non-linear parabolic equations by implicit difference methods*, Quart. Appl. Math.**14**(1956), 237–248. MR**0085610**

Retrieve articles in *Transactions of the American Mathematical Society*
with MSC:
65.68

Retrieve articles in all journals with MSC: 65.68

Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1959-0141235-6

Article copyright:
© Copyright 1959
American Mathematical Society