Application of thin plate splines for solving a class of boundary integral equations arisen from Laplace's equations with nonlinear boundary conditions

DOI10.1080/00207160.2017.1420786zbMath1499.65706OpenAlexW2778814528MaRDI QIDQ5031802

Pouria Assari, Mehdi Dehghan

Publication date: 16 February 2022

Published in: International Journal of Computer Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/00207160.2017.1420786

zbMATH Keywords

error analysismeshless methodLaplace's equationthin plate splinediscrete collocation methodnonlinear boundary integral equation

Mathematics Subject Classification ID

Spectral and related methods applied to problems in solid mechanics (74S25) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Boundary element methods for boundary value problems involving PDEs (65N38) Singular nonlinear integral equations (45G05) Nonlinear boundary value problems for nonlinear elliptic equations (35J66)

Related Items (7)

Meshless local radial point interpolation (MLRPI) to two dimensional wave equation with Neumann’s boundary conditions ⋮ The modified quadrature method for Laplace equation with nonlinear boundary conditions ⋮ Green's function and surface waves in a viscoelastic orthotropic FGM enforced by an impulsive point source ⋮ A local meshfree radial point interpolation method for Berger equation arising in modelling of thin plates ⋮ The numerical solution of nonlinear delay Volterra integral equations using the thin plate spline collocation method with error analysis ⋮ On the Numerical Solution of Logarithmic Boundary Integral Equations Arising in Laplace's Equations Based on the Meshless Local Discrete Collocation Method ⋮ An accurate a posteriori error estimator for semilinear Neumann problem and its applications

Cites Work

• Unnamed Item
• Unnamed Item
• An explicit kernel-split panel-based Nyström scheme for integral equations on axially symmetric surfaces
• Recent advances on radial basis function collocation methods
• A meshless discrete Galerkin (MDG) method for the numerical solution of integral equations with logarithmic kernels
• Numerical solution of nonlinear Volterra-Fredholm-Hammerstein integral equations via collocation method based on radial basis functions
• A meshless method based on the moving least squares (MLS) approximation for the numerical solution of two-dimensional nonlinear integral equations of the second kind on non-rectangular domains
• Mechanical quadrature methods and extrapolation for solving nonlinear boundary Helmholtz integral equations
• A meshless based method for solution of integral equations
• A Galerkin boundary node method and its convergence analysis
• Multivariate interpolation at arbitrary points made simple
• Local accuracy for radial basis function interpolation on finite uniform grids
• On condition numbers associated with radial-function interpolation
• An implementation of fast wavelet Galerkin methods for integral equations of the second kind
• Method of approximate particular solutions for constant- and variable-order fractional diffusion models
• Galerkin trigonometric wavelet methods for the natural boundary integral equations
• A meshless method for solving nonlinear two-dimensional integral equations of the second kind on non-rectangular domains using radial basis functions with error analysis
• Boundary particle method for Laplace transformed time fractional diffusion equations
• The numerical solution of weakly singular integral equations based on the meshless product integration (MPI) method with error analysis
• Trigonometric Hermite wavelet approximation for the integral equations of second kind with weakly singular kernel
• Wavelet approximations for first kind boundary integral equations on polygons
• Boundary Integral Equation Methods for Solving Laplace's Equation with Nonlinear Boundary Conditions: The Smooth Boundary Case
• Wavelet numerical solutions for weakly singular Fredholm integral equations of the second kind
• Scattered Data Interpolation: Tests of Some Method
• Gauss-Type Quadratures for Weakly Singular Integrals and their Application to Fredholm Integral Equations of the Second Kind
• A Fast Numerical Solution for a Second Kind Boundary Integral Equation with a Logarithmic Kernel
• The Numerical Solution of Integral Equations of the Second Kind
• Radial Basis Functions
• A Spectral Galerkin Method for a Boundary Integral Equation
• Piecewise Polynomial Collocation for Boundary Integral Equations
• Wavelet Galerkin Schemes for Boundary Integral Equations---Implementation and Quadrature
• The Numerical Evaluation of Fixed Points for Completely Continuous Operators
• Scattered Data Approximation
• Nonlinear boundary integral equations for harmonic problems

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