The application of stability analysis in the numerical solution of quasi-linear parabolic differential equations
HTML articles powered by AMS MathViewer
- by Jim Douglas PDF
- Trans. Amer. Math. Soc. 89 (1958), 484-518 Request permission
References
-
R. Courant and D. Hilbert, Methods of mathematical physics, vol. 1, New York, 1953.
- Jim Douglas Jr., On the numerical integration of $\partial ^2u/\partial x^2+\partial ^2u/\partial y^2=\partial u/\partial t$ by implicit methods, J. Soc. Indust. Appl. Math. 3 (1955), 42β65. MR 71875
- Jim Douglas Jr., On the numerical integration of quasilinear parabolic differential equations, Pacific J. Math. 6 (1956), 35β42. MR 79196
- Jim Douglas Jr., The solution of the diffusion equation by a high order correct difference equation, J. Math. and Phys. 35 (1956), 145β151. MR 90875, DOI 10.1002/sapm1956351145
- 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), 20β37. MR 80368 β, A note on the numerical solution of parabolic differential equations, to appear. J. Douglas, Jr., D. W. Peaceman, and H. H. Rachford, Jr., Calculation of unsteady-state gas flow within a square drainage area, Trans. Amer. Inst. Mining, Metallurgical, and Petroleum Engineers, vol. 204 (1955) pp. 190-195.
- Jim Douglas Jr. and H. H. Rachford Jr., On the numerical solution of heat conduction problems in two and three space variables, Trans. Amer. Math. Soc. 82 (1956), 421β439. MR 84194, DOI 10.1090/S0002-9947-1956-0084194-4
- Paul R. Halmos, Finite Dimensional Vector Spaces, Annals of Mathematics Studies, No. 7, Princeton University Press, Princeton, N.J., 1942. MR 0006591
- M. R. Hestenes and W. Karush, Solutions of $Ax=\lambda Bx$, J. Research Nat. Bur. Standards 47 (1951), 471β478. MR 0049852
- 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), 155β211. MR 47885, DOI 10.1002/cpa.3160050203 M. L. Juncosa and D. Young, On the Crank-Nicolson procedure for parabolic differential equations, Bull. Amer. Math. Soc. Abstract 60-2-240.
- P. D. Lax and R. D. Richtmyer, Survey of the stability of linear finite difference equations, Comm. Pure Appl. Math. 9 (1956), 267β293. MR 79204, DOI 10.1002/cpa.3160090206
- Solomon Lefschetz, Introduction to Topology, Princeton Mathematical Series, vol. 11, Princeton University Press, Princeton, N. J., 1949. MR 0031708
- William Edmund Milne, Numerical solution of differential equations, John Wiley & Sons, Inc., New York; Chapman & Hall, Ltd., London, 1953. MR 0068321
- George G. OβBrien, Morton A. Hyman, and Sidney Kaplan, A study of the numerical solution of partial differential equations, J. Math. Physics 29 (1951), 223β251. MR 0040805
- D. W. Peaceman and H. H. Rachford Jr., The numerical solution of parabolic and elliptic differential equations, J. Soc. Indust. Appl. Math. 3 (1955), 28β41. MR 71874 A. Zygmund, Trigonometrical series, Warsaw-Lwow, 1935.
Additional Information
- © Copyright 1958 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 89 (1958), 484-518
- MSC: Primary 65.68; Secondary 35.65
- DOI: https://doi.org/10.1090/S0002-9947-1958-0131673-9
- MathSciNet review: 0131673