Numerical Methods for Partial Differential Equations · 2020 · 23 citations · 11 references
Natural SciencesComputational EngineeringComputational MechanicsComputational PhysicsDifferential EquationsBoundary-value ProblemsConvergence AnalysisNumerical AlgorithmsNumerical AnalysisNumerical Methods For Differential EquationsPartial Differential EquationsBoundary Value Problem SolversConvergence Rate AnalysisNumerical Analysis Of Partial Differential EquationsNumerical Solutions Of Partial Differential EquationsPartial Differential Equation SolversPoisson EquationPoisson's Equation
Abstract Two‐dimensional biharmonic boundary‐value problems are considered by the linear barycentric rational method, the unknown function was approximated by the barycentric rational function. For the biharmonic equation, we change the biharmonic equation into the two Poisson equations by depression of order. The linear equations of discrete the biharmonic equation was changed into matrix form. For the basis of barycentric rational function, we present the convergence rate of linear barycentric rational method for biharmonic equation by depression of order. At last, several numerical examples are provided to validate the theoretical analysis.
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