On the integration of non-linear parabolic equations by implicit difference methods-Reference-Cited by-同舟云学术

On the integration of non-linear parabolic equations by implicit difference methods

Published:1956 Issue:3 Volume:14 Page:237-248
ISSN:0033-569X
Container-title:Quarterly of Applied Mathematics
language:en
Short-container-title:Quart. Appl. Math.

Author:

Rose Milton E.

Abstract

The object of this paper is to investigate how solutions of mixed initial-boundary value problems for a certain class of non-linear parabolic equations may be obtained by solving suitable implicit difference equations on a rectangular lattice and taking the limit of such solutions as the mesh of the lattice tends to zero.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics

Link

http://www.ams.org/qam/1956-14-03/S0033-569X-1956-85610-4/S0033-569X-1956-85610-4.pdf

Reference8 articles.

1. On integration of parabolic equations by difference methods. I. Linear and quasi-linear equations for the infinite interval;John, Fritz;Comm. Pure Appl. Math.,1952

2. R. P. Eddy, Stability in the numerical solution of initial value problems in partial differential equations, NOLM 10232, (1949)

3. A study of the numerical solution of partial differential equations;O’Brien, George G.;J. Math. Physics,1951

4. On mildly nonlinear partial difference equations of elliptic type;Bers, Lipman;J. Research Nat. Bur. Standards,1953

5. S. Gerschgorin, Fehlerabschätzung für das Differenzenverfahren zur Lösung partieller Differentialgleichungen, Z. Angew. Math. Mech. 10, 373-382 (1930)

Cited by 24 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. An analysis for a high-order difference scheme for numerical solution touxx =F(x, t, u, ut, ux);Numerical Methods for Partial Differential Equations;2006

2. The Backward Euler Method for Numerical Solution of the Hodgkin–Huxley Equations of Nerve Conduction;SIAM Journal on Numerical Analysis;1990-08

3. Finite difference methods for linear parabolic equations;Handbook of Numerical Analysis Volume 1;1990

4. Monotone iterative methods for finite difference system of reaction-diffusion equations;Numerische Mathematik;1985-12

5. Implicit difference method for solving the first boundary-value problem for a second-order nonlinear parabolic equation;Journal of Soviet Mathematics;1977-01