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Fast Numerical Solution of the Biharmonic Dirichlet Problem on Rectangles

https://doi.org/10.1137/0720004

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inferred← citeshttps://doi.org/10.1016/j.advengsoft.2006.08.007openalex-snapshot

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inferred← citeshttps://doi.org/10.1016/j.apm.2015.01.006openalex-snapshot

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inferred← citeshttps://doi.org/10.1016/j.apnum.2007.07.001openalex-snapshot

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inferred← citeshttps://doi.org/10.1016/j.enganabound.2019.10.007openalex-snapshot

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inferred← citeshttps://doi.org/10.1016/j.enganabound.2023.06.008openalex-snapshot

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inferred← citeshttps://doi.org/10.1016/j.jcp.2003.08.010openalex-snapshot

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inferred← citeshttps://doi.org/10.1016/j.jcp.2006.03.014openalex-snapshot

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inferred← citeshttps://doi.org/10.1016/j.jcp.2025.114254openalex-snapshot

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inferred← citeshttps://doi.org/10.1016/s0168-2024(99)80012-5openalex-snapshot

References

inferred← citeshttps://doi.org/10.1016/s0252-9602(14)60115-6openalex-snapshot

On solvability of a boundary value problem for a nonhomogeneous biharmonic equation with a boundary operator of a fractional order

inferred← citeshttps://doi.org/10.1016/s0252-9602(16)30043-1openalex-snapshot

On some boundary value problems for nonhomogenous polyharmonic equation with boundary operators of fractional order

inferred← citeshttps://doi.org/10.1016/s0377-0427(00)00509-4openalex-snapshot

Orthogonal spline collocation methods for partial differential equations

inferred← citeshttps://doi.org/10.1016/s0377-0427(98)00079-xopenalex-snapshot

Solution of biharmonic equations with application to radar imaging

inferred← citeshttps://doi.org/10.1016/s0747-7171(08)80050-8openalex-snapshot

Uses Made of Computer Algebra in Physics

inferred← citeshttps://doi.org/10.1016/s0927-7757(01)00829-9openalex-snapshot

Electrically-driven fluid motion in channels with streamwise gradients of the electrical conductivity

inferred← citeshttps://doi.org/10.1016/s1570-8659(03)09003-3openalex-snapshot

Finite element methods for incompressible viscous flow

inferred← citeshttps://doi.org/10.1017/s0022112006003867openalex-snapshot

Lubrication theory for electro-osmotic flow in a non-uniform electrolyte

inferred← citeshttps://doi.org/10.1051/m2an/1988220406551openalex-snapshot

On the numerical solution of the first biharmonic equation

inferred← citeshttps://doi.org/10.1051/m2an:2001117openalex-snapshot

Vorticity dynamics and numerical Resolution of Navier-Stokes Equations

inferred← citeshttps://doi.org/10.1080/00207169108804013openalex-snapshot

An approximate inverse based multigrid approach to the biharmonic problem

inferred← citeshttps://doi.org/10.1080/00207169308804233openalex-snapshot

Orthogonal collocation solution of biharmonic equations

inferred← citeshttps://doi.org/10.1080/02533839.2000.9670520openalex-snapshot

An integrated design environment for 3‐D geometric modeling of shipbuilding engineering

inferred← citeshttps://doi.org/10.1080/03081088908817925openalex-snapshot

Closure, commutativity and minimal complexity of some spaces of matrices

inferred← citeshttps://doi.org/10.1080/10556788.2012.733004openalex-snapshot

Solving nonlinear equations with the Newton–Krylov method based on automatic differentiation

inferred← citeshttps://doi.org/10.1088/1742-6596/1212/1/012021openalex-snapshot

Solving boundary problems for biharmonic operator by using Integro-differential operators of fractional order

inferred← citeshttps://doi.org/10.1090/conm/323/05707openalex-snapshot

High order accurate particular solutions of the biharmonic equation on general regions

inferred← citeshttps://doi.org/10.1093/imanum/drv033openalex-snapshot

The FFTRR-based fast decomposition methods for solving complex biharmonic problems and incompressible flows

inferred← citeshttps://doi.org/10.1103/physreva.30.398openalex-snapshot

Nonlinear pattern formation near the onset of Rayleigh-Bénard convection

inferred← citeshttps://doi.org/10.1103/physreve.63.045201openalex-snapshot

Finite size scaling of domain chaos

inferred← citeshttps://doi.org/10.1103/physreve.64.046204openalex-snapshot

Pattern formation near onset of a convecting fluid in an annulus

inferred← citeshttps://doi.org/10.1109/jproc.2018.2799702openalex-snapshot

Graph Spectral Image Processing

inferred← citeshttps://doi.org/10.1109/rusautocon49822.2020.9208198openalex-snapshot

Investigation of a Mixed Boundary Value Problem for the Poisson Equation

inferred← citeshttps://doi.org/10.1111/j.1749-6632.1990.tb22751.xopenalex-snapshot

Numerical Computation: The State of the Art

inferred← citeshttps://doi.org/10.1134/s0001434617070045openalex-snapshot

On the Dirichlet–Riquier problem for biharmonic equations

inferred← citeshttps://doi.org/10.1137/0610004openalex-snapshot

A Matrix Decomposition Method for Orthotropic Elasticity Problems

inferred← citeshttps://doi.org/10.1137/070694168openalex-snapshot

A Fast Direct Solver for the Biharmonic Problem in a Rectangular Grid

inferred← citeshttps://doi.org/10.1137/0723075openalex-snapshot

Iterative Methods for the Solution of Elliptic Problems on Regions Partitioned into Substructures

inferred← citeshttps://doi.org/10.1137/080718784openalex-snapshot

A Compact Difference Scheme for the Biharmonic Equation in Planar Irregular Domains

inferred← citeshttps://doi.org/10.1137/0911026openalex-snapshot

Hybrid Krylov Methods for Nonlinear Systems of Equations

inferred← citeshttps://doi.org/10.1137/0915089openalex-snapshot

Efficient Spectral-Galerkin Method I. Direct Solvers of Second- and Fourth-Order Equations Using Legendre Polynomials

inferred← citeshttps://doi.org/10.1137/0917003openalex-snapshot

Choosing the Forcing Terms in an Inexact Newton Method

inferred← citeshttps://doi.org/10.1137/15m1014887openalex-snapshot

Efficient Block Preconditioning for a $C^1$ Finite Element Discretization of the Dirichlet Biharmonic Problem

inferred← citeshttps://doi.org/10.1137/19m1254313openalex-snapshot

Optimal-Order Finite Difference Approximation of Generalized Solutions to the Biharmonic Equation in a Cube

inferred← citeshttps://doi.org/10.1137/s1064827596298233openalex-snapshot

Timely Communication: Efficient Algorithms for Solving a Fourth-Order Equation with the Spectral-Galerkin Method

inferred← citeshttps://doi.org/10.1137/s1064827596303843openalex-snapshot

NITSOL: A Newton Iterative Solver for Nonlinear Systems

inferred← citeshttps://doi.org/10.1145/140682.140686openalex-snapshot

The role of computer software in numerical analysis teaching

inferred← citeshttps://doi.org/10.1155/2018/3950312openalex-snapshot

On Surface Completion and Image Inpainting by Biharmonic Functions: Numerical Aspects

inferred← citeshttps://doi.org/10.13182/nse90-a23743openalex-snapshot

Application of Krylov Subspace Methods in Fluid Dynamics

inferred← citeshttps://doi.org/10.21236/ada444064openalex-snapshot

A Fast Finite Difference Method for Biharmonic Equations on Irregular Domains

inferred← citeshttps://doi.org/10.26192/q35qxopenalex-snapshot

Parallel computations based on domain decompositions and integrated radial basis functions for fluid flow problems

inferred← citeshttps://doi.org/10.3103/s1068362313020052openalex-snapshot

On an effective solution of the Riemann problem for third order improperly elliptic equations

inferred← citeshttps://doi.org/10.3390/math11020420openalex-snapshot

A Review of Mathematical Models of Elasticity Theory Based on the Methods of Iterative Factorizations and Fictitious Components

inferred← citeshttps://doi.org/10.3970/cmes.2012.084.171openalex-snapshot

Several compact local stencils based on integrated RBFs for fourth-order ODEs and PDEs

inferred← citeshttps://doi.org/10.4208/aamm.2012.m69openalex-snapshot

An Efficient Numerical Solution Method for Elliptic Problems in Divergence Form

inferred← citeshttps://doi.org/10.4213/mzm11035openalex-snapshot

О задаче Дирихле-Рикье для бигармонического уравнения

inferred← citeshttps://doi.org/10.4236/ajcm.2012.24038openalex-snapshot

Effective Solution of Riemann Problem for Fifth Order Improperly Elliptic Equation on a Rectangle

inferred← citeshttps://doi.org/10.58491/2735-4202.3173openalex-snapshot

Numerical Solution of Biharmonic Equation Using Modified Bi-Quintic B-Spline Collocation Method

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