Linear barycentric rational collocation method for solving biharmonic equation
Jin Li
Abstract
Abstract Two-dimensional biharmonic boundary-value problems are considered by the linear barycentric rational collocation method, and the unknown function is approximated by the barycentric rational polynomial. With the help of matrix form, the linear equations of the discrete biharmonic equation are changed into a matrix equation. From the convergence rate of barycentric rational polynomial, we present the convergence rate of linear barycentric rational collocation method for biharmonic equation. Finally, several numerical examples are provided to validate the theoretical analysis.
Topics & Concepts
Barycentric coordinate systemBiharmonic equationMathematicsMathematical analysisCollocation methodRate of convergenceRational functionPolynomialCollocation (remote sensing)Applied mathematicsBoundary value problemGeometryOrdinary differential equationDifferential equationElectrical engineeringEngineeringRemote sensingChannel (broadcasting)GeologyFractional Differential Equations SolutionsNumerical methods in engineeringIterative Methods for Nonlinear Equations