Previous article Next article The Coupled Equation Approach to the Numerical Solution of the Biharmonic Equation by Finite Differences. IIJulius SmithJulius Smithhttps://doi.org/10.1137/0707005PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout Previous article Next article FiguresRelatedReferencesCited byDetails Regularization of a final value problem for a linear and nonlinear biharmonic equation with observed data in Lq spaceAIMS Mathematics, Vol. 7, No. 12 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 Fourth-Order Compact Finite Difference Scheme for Higher-Order PDE-Based Image Registration10 November 2015 | East Asian Journal on Applied Mathematics, Vol. 5, No. 4 Cross Ref A new high accuracy method for two-dimensional biharmonic equation with nonlinear third derivative terms: application to Navier–Stokes equations of motion20 August 2014 | International Journal of Computer Mathematics, Vol. 92, No. 8 Cross Ref Sinc-Galerkin method for solving biharmonic problemsApplied Mathematics and Computation, Vol. 247 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 New High Accuracy Off-Step Discretisation for the Solution of 2D Nonlinear Triharmonic Equations28 May 2015 | East Asian Journal on Applied Mathematics, Vol. 3, No. 3 Cross Ref A fourth order finite difference method for the Dirichlet biharmonic problem20 January 2012 | Numerical Algorithms, Vol. 61, No. 3 Cross Ref A Novel Numerical Method of for Three-Dimensional Non-Linear Triharmonic Equations20 August 2015 | Communications in Computational Physics, Vol. 12, No. 5 Cross Ref A compact discretization of O ( h4 ) for two-dimensional nonlinear triharmonic equations4 July 2011 | Physica Scripta, Vol. 84, No. 2 Cross Ref The First Biharmonic Steklov Eigenvalue: Positivity Preserving and Shape Optimization28 May 2011 | Milan Journal of Mathematics, Vol. 79, No. 1 Cross Ref A New Fourth Order Difference Approximation for the Solution of Three-dimensional Non-linear Biharmonic Equations Using Coupled ApproachAmerican Journal of Computational Mathematics, Vol. 01, No. 04 Cross Ref Single-cell compact finite-difference discretization of order two and four for multidimensional triharmonic problems29 June 2009 | Numerical Methods for Partial Differential Equations, Vol. 26, No. 6 Cross Ref A new high accuracy finite difference discretization for the solution of 2D nonlinear biharmonic equations using coupled approach23 April 2009 | Numerical Methods for Partial Differential Equations, Vol. 26, No. 4 Cross Ref A new coupled approach high accuracy numerical method for the solution of 3D non-linear biharmonic equationsApplied Mathematics and Computation, Vol. 215, No. 8 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)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 Solution of biharmonic equations with application to radar imagingJournal of Computational and Applied Mathematics, Vol. 94, No. 2 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 The Fast Solution of Poisson’s and the Biharmonic Equations on Irregular RegionsAnita Mayo17 July 2006 | SIAM Journal on Numerical Analysis, Vol. 21, No. 2AbstractPDF (1665 KB)Fast Numerical Solution of the Biharmonic Dirichlet Problem on RectanglesPetter Bjørstad17 July 2006 | SIAM Journal on Numerical Analysis, Vol. 20, No. 1AbstractPDF (1204 KB)EFFICIENT SOLUTION OF THE BIHARMONIC EQUATION Cross Ref References Cross Ref Numerical Methods for the First Biharmonic Equation and for the Two-Dimensional Stokes ProblemR. Glowinski and O. Pironneau17 February 2012 | SIAM Review, Vol. 21, No. 2AbstractPDF (3561 KB)The Direct Solution of the Biharmonic Equation on Rectangular Regions and the Poisson Equation on Irregular RegionsB. L. Buzbee and Fred W. Dorr14 July 2006 | SIAM Journal on Numerical Analysis, Vol. 11, No. 4AbstractPDF (1018 KB)A General Coupled Equation Approach for Solving the Biharmonic Boundary Value ProblemJohnnie William McLaurin14 July 2006 | SIAM Journal on Numerical Analysis, Vol. 11, No. 1AbstractPDF (1260 KB)Solving the biharmonic equation in a squareCommunications of the ACM, Vol. 16, No. 11 Cross Ref On the Convergence of Two-Stage Iterative Processes for Solving Linear EquationsNancy K. Nichols14 July 2006 | SIAM Journal on Numerical Analysis, Vol. 10, No. 3AbstractPDF (776 KB)Remarks on a Stekloff Eigenvalue ProblemJames R. Kuttler1 August 2006 | SIAM Journal on Numerical Analysis, Vol. 9, No. 1AbstractPDF (336 KB)Coupled harmonic equations, SOR, and Chebyshev acceleration1 January 1972 | Mathematics of Computation, Vol. 26, No. 118 Cross Ref Solving the Biharmonic Equation as Coupled Finite Difference EquationsLouis W. Ehrlich14 July 2006 | SIAM Journal on Numerical Analysis, Vol. 8, No. 2AbstractPDF (522 KB) Volume 7, Issue 1| 1970SIAM Journal on Numerical Analysis History Submitted:28 March 1986Published online:14 July 2006 InformationCopyright © 1970 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0707005Article page range:pp. 104-111ISSN (print):0036-1429ISSN (online):1095-7170Publisher:Society for Industrial and Applied Mathematics
No takes yet. Share an insight, caveat, or question.
Julius O. Smith (1970) studied this question.
Synapse has enriched one closely related paper. Consider it for comparative context: