Some stable difference approximations to a fourth-order parabolic partial differential equation
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- by G. Fairweather and A. R. Gourlay PDF
- Math. Comp. 21 (1967), 1-11 Request permission
Corrigendum: Math. Comp. 22 (1968), 246-247.
References
- Garrett Birkhoff, Richard S. Varga, and David Young, Alternating direction implicit methods, Advances in Computers, Vol. 3, Academic Press, New York, 1962, pp. 189–273. MR 0168131
- J. Crank and P. Nicolson, A practical method for numerical evaluation of solutions of partial differential equations of the heat-conduction type, Proc. Cambridge Philos. Soc. 43 (1947), 50–67. MR 19410
- Jim Douglas Jr., The solution of the diffusion equation by a high order correct difference equation, J. Math. and Phys. 35 (1956), 145–151. MR 90875, DOI 10.1002/sapm1956351145 E. C. Du Fort & S. P. Frankel, "Stability conditions in the numerical treatment of parabolic differential equations," MTAC, v. 7, 1953, pp. 135–152. MR 15, 474.
- D. J. Evans, A stable explicit method for the finite-difference solution of a fourth-order parabolic partial differential equation, Comput. J. 8 (1965), 280–287. MR 189264, DOI 10.1093/comjnl/8.3.280
- Heinz-Otto Kreiss, Über implizite Differenzmethoden für partielle Differentialgleichungen, Numer. Math. 5 (1963), 24–47 (German). MR 155442, DOI 10.1007/BF01385876
- Milton Lees, Alternating direction and semi-explicit difference methods for parabolic partial differential equations, Numer. Math. 3 (1961), 398–412. MR 142212, DOI 10.1007/BF01386038
- A. R. Mitchell and G. Fairweather, Improved forms of the alternating direction methods of Douglas, Peaceman, and Rachford for solving parabolic and elliptic equations, Numer. Math. 6 (1964), 285–292. MR 174184, DOI 10.1007/BF01386076 B. Numerov, Publ. Observ. Astrophys. Central Russia, v. 2, 1933, p. 188.
- D. W. Peaceman and H. H. Rachford Jr., The numerical solution of parabolic and elliptic differential equations, J. Soc. Indust. Appl. Math. 3 (1955), 28–41. MR 71874
- Robert D. Richtmyer, Difference methods for initial-value problems, Interscience Tracts in Pure and Applied Mathematics, Tract 4, Interscience Publishers, Inc., New York, 1957. MR 0093918
- Jim Douglas Jr., The application of stability analysis in the numerical solution of quasi-linear parabolic differential equations, Trans. Amer. Math. Soc. 89 (1958), 484–518. MR 131673, DOI 10.1090/S0002-9947-1958-0131673-9
- Milton Lees, A priori estimates for the solutions of difference approximations to parabolic partial differential equations, Duke Math. J. 27 (1960), 297–311. MR 121998
- Richard S. Varga, Matrix iterative analysis, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1962. MR 0158502 G. Fairweather & A. R. Mitchell, "Some computational results of an improved ADI method for the Dirichlet problem," Comput. J. (To appear.)
Additional Information
- © Copyright 1967 American Mathematical Society
- Journal: Math. Comp. 21 (1967), 1-11
- MSC: Primary 65.68
- DOI: https://doi.org/10.1090/S0025-5718-1967-0221785-2
- MathSciNet review: 0221785