The Numerical Solution of Parabolic and Elliptic Differential Equations (1955)

Previous article Next article The Numerical Solution of Parabolic and Elliptic Differential EquationsD. W. Peaceman and H. H. Rachford, Jr.D. W. Peaceman and H. H. Rachford, Jr.https://doi.org/10.1137/0103003PDFPDF PLUSBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] G. H., Bruce, , D. W., Peaceman, , H. H., Rachford and , J. D. Rice, Calculation of unsteady-state gas flow through porous media, Trans. Amer. Inst. Mining and Met. Engrs., 198 (1953), 79– ISIGoogle Scholar[2] H. S. Carslaw and , J. C. Jaeger, Conduction of Heat in Solids, Oxford, at the Clarendon Press, 1947viii+386 MR0022294 Google Scholar[3] Stanley P. Frankel, Convergence rates of iterative treatments of partial differential equations, Math. Tables and Other Aids to Computation, 4 (1950), 65–75 MR0046149 CrossrefGoogle Scholar[4] 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 MR0040805 0042.13204 CrossrefISIGoogle Scholar[5] Jim Douglas, Jr., On the numerical integration of $\partial\sp 2u/\partial x\sp 2+\partial\sp 2u/\partial y\sp 2=\partial u/\partial t$ by implicit methods, J. Soc. Indust. Appl. Math., 3 (1955), 42–65 10.1137/0103004 MR0071875 0067.35802 LinkISIGoogle Scholar[6] Jim Douglas, Jr. and , T. M. Gallie, Jr., Variable time steps in the solution of the heat flow equation by a difference equation, Proc. Amer. Math. Soc., 6 (1955), 787–793 MR0078754 0066.10502 CrossrefGoogle Scholar[7] J. Douglas, Jr. and , D. W. Peaceman, Numerical solution of two-dimensional heat flow problems, to be presented at the May, 1955 meeting of The American Institute of Chemical Engineers at Houston, Texas Google Scholar Previous article Next article FiguresRelatedReferencesCited ByDetails A General Alternating-Direction Implicit Framework with Gaussian Process Regression Parameter Prediction for Large Sparse Linear SystemsKai Jiang, Xuehong Su, and Juan ZhangSIAM Journal on Scientific Computing, Vol. 44, No. 4 | 7 July 2022AbstractPDF (1383 KB)Convergence Analysis of the Nonoverlapping Robin--Robin Method for Nonlinear Elliptic EquationsEmil Engström and Eskil HansenSIAM Journal on Numerical Analysis, Vol. 60, No. 2 | 21 March 2022AbstractPDF (565 KB)Robust Alternating Direction Implicit Solver in Quantized Tensor Formats for a Three-Dimensional Elliptic PDEM. 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