The Coupled Equation Approach to the Numerical Solution of the Biharmonic Equation by finite Differences. I

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Previous article Next article The Coupled Equation Approach to the Numerical Solution of the Biharmonic Equation by finite Differences. IJulius SmithJulius Smithhttps://doi.org/10.1137/0705028PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] R. E. Esch, An alternative method of handling boundary conditions and various computational experiments in the numerical solution of viscous flow problems, Tech. Rep., SRRC-RR-64-64, Sperry Rand Research Center, Sudbury, Massachusetts, 1964 Google Scholar[2] George E. Forsythe and , Wolfgang R. Wasow, Finite-difference methods for partial differential equations, Applied Mathematics Series, John Wiley & Sons Inc., New York, 1960x+444 MR0130124 (23:B3156) 0099.11103 Google Scholar[3] Kurt Friedrichs, Die Randwert-und Eigenwertprobleme aus der Theorie der elastischen Platten. (Anwendung der direkten Methoden der Variationsrechnung), Math. 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Anal., 4 (1967), 626–639 MR0220456 (36:3516) 0155.21303 LinkGoogle Scholar Previous article Next article FiguresRelatedReferencesCited byDetails Convergence of two-stage iterative scheme for K -weak regular splittings of type IIApplied Mathematics and Computation, Vol. 410 Cross Ref A fast Fourier–Galerkin method solving a system of integral equations for the biharmonic equationJournal of Integral Equations and Applications, Vol. 33, No. 4 Cross Ref Optimal-Order Finite Difference Approximation of Generalized Solutions to the Biharmonic Equation in a CubeStefan Müller, Florian Schweiger, and Endre Süli14 January 2020 | SIAM Journal on Numerical Analysis, Vol. 58, No. 1AbstractPDF (559 KB)A Fully Discrete Fast Fourier–Galerkin Method Solving a Boundary Integral Equation for the Biharmonic Equation26 March 2018 | Journal of Scientific Computing, Vol. 76, No. 3 Cross Ref A new coupled high-order compact method for the three-dimensional nonlinear biharmonic equations26 March 2014 | International Journal of Computer Mathematics, Vol. 91, No. 10 Cross Ref A Fast Fourier--Galerkin Method Solving a Boundary Integral Equation for the Biharmonic EquationYing Jiang, Bo Wang, and Yuesheng Xu16 October 2014 | SIAM Journal on Numerical Analysis, Vol. 52, No. 5AbstractPDF (561 KB)A fourth order finite difference method for the Dirichlet biharmonic problem20 January 2012 | Numerical Algorithms, Vol. 61, No. 3 Cross Ref 9.12 Interactions of the Cell Membrane with Integral Proteins Cross Ref Quantitative Modeling of Membrane Deformations by Multihelical Membrane Proteins: Application to G-Protein Coupled ReceptorsBiophysical Journal, Vol. 101, No. 9 Cross Ref The First Biharmonic Steklov Eigenvalue: Positivity Preserving and Shape Optimization28 May 2011 | Milan Journal of Mathematics, Vol. 79, No. 1 Cross Ref Numerical performance of parallel group explicit solvers for the solution of fourth order elliptic equationsApplied Mathematics and Computation, Vol. 217, No. 6 Cross Ref On the first eigenvalue of a fourth order Steklov problem12 July 2008 | Calculus of Variations and Partial Differential Equations, Vol. 35, No. 1 Cross Ref A fast finite difference method for biharmonic equations on irregular domains and its application to an incompressible Stokes flow24 July 2007 | Advances in Computational Mathematics, Vol. 29, No. 2 Cross Ref A Fast Direct Solver for the Biharmonic Problem in a Rectangular GridMatania Ben-Artzi, Jean-Pierre Croisille, and Dalia Fishelov16 October 2008 | SIAM Journal on Scientific Computing, Vol. 31, No. 1AbstractPDF (305 KB)An expansion of the solution of Dirichlet boundary value problem for Berger equationJournal of Computational and Applied Mathematics, Vol. 193, No. 1 Cross Ref On a fourth order Steklov eigenvalue problemAnalysis, Vol. 25, No. 4 Cross Ref Numerical Techniques for Solving a Biharmonic Equation in a Sectorial Region Cross Ref Explicit preconditioned conjugate gradient schemes for solving biharmonic equationsEngineering Computations, Vol. 17, No. 2 Cross Ref Scalable Poisson and VLSI Biharmonic Solvers Cross Ref A scalable VLSI algorithm for the fourth-order elliptic problem Cross Ref Fast serial algorithms for solving biharmonic equation Cross Ref Orthogonal collocation solution of biharmonic equationsInternational Journal of Computer Mathematics, Vol. 49, No. 3-4 Cross Ref A coupled double splitting ADI scheme for the first biharmonic using collocationNumerical Methods for Partial Differential Equations, Vol. 6, No. 4 Cross Ref A numerical case study of a non-Newtonian flow problemInternational Journal for Numerical Methods in Engineering, Vol. 26, No. 3 Cross Ref SOR methods for coupled elliptic partial differential equationsJournal of Computational Physics, Vol. 71, No. 1 Cross Ref Iterative methods for the parallel solution of linear systemsComputers & Mathematics with Applications, Vol. 13, No. 7 Cross Ref On the convergence of Uzawa's method for the solution of biharmonic problemCalcolo, Vol. 20, No. 4 Cross Ref Fast Numerical Solution of the Biharmonic Dirichlet Problem on RectanglesPetter Bjørstad17 July 2006 | SIAM Journal on Numerical Analysis, Vol. 20, No. 1AbstractPDF (1204 KB)Acceleration of the convergence in viscous flow computationsJournal of Computational Physics, Vol. 43, No. 1 Cross Ref EFFICIENT SOLUTION OF THE BIHARMONIC EQUATION Cross Ref References Cross Ref A mixed finite element solution of some biharmonic unilateral problem15 May 2007 | Numerical Functional Analysis and Optimization, Vol. 2, No. 5 Cross Ref Direct solution of the biharmonic equation using noncoupled approachJournal of Computational Physics, Vol. 33, No. 2 Cross Ref Numerical Methods for the First Biharmonic Equation and for the Two-Dimensional Stokes ProblemR. 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