A meshless discrete Galerkin (MDG) method for the numerical solution of integral equations with logarithmic kernels

DOI10.1016/j.cam.2014.01.037zbMath1293.65166OpenAlexW2072025015MaRDI QIDQ396047

Pouria Assari, Hojatollah Adibi, Mehdi Dehghan

Publication date: 8 August 2014

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2014.01.037

zbMATH Keywords

error analysisboundary integral equationmeshless methoddiscrete Galerkin methodmoving least squares (MLS) approximationlogarithmic integral equation

Mathematics Subject Classification ID

Numerical methods for integral equations (65R20) Spectral and related methods applied to problems in solid mechanics (74S25) Fredholm integral equations (45B05)

Related Items (30)

Application of thin plate splines for solving a class of boundary integral equations arisen from Laplace's equations with nonlinear boundary conditions ⋮ Collocation method for generalized Abel's integral equations ⋮ Solving Fredholm integral equations via a piecewise linear maximum entropy method ⋮ The approximate solution of nonlinear Volterra integral equations of the second kind using radial basis functions ⋮ An interpolation-based method for solving Volterra integral equations ⋮ More accurate results for nonlinear generalized Benjamin-Bona-Mahony-Burgers (GBBMB) problem through spectral meshless radial point interpolation (SMRPI) ⋮ The combination of meshless method based on radial basis functions with a geometric numerical integration method for solving partial differential equations: application to the heat equation ⋮ Numerical simulation based on meshless technique to study the biological population model ⋮ Error analysis in Sobolev spaces for the improved moving least-square approximation and the improved element-free Galerkin method ⋮ The numerical solution of Fredholm-Hammerstein integral equations by combining the collocation method and radial basis functions ⋮ Solving a class of nonlinear boundary integral equations based on the meshless local discrete Galerkin (MLDG) method ⋮ Discrete collocation method for Volterra type weakly singular integral equations with logarithmic kernels ⋮ The numerical solution of nonlinear integral equations of the second kind using thin plate spline discrete collocation method ⋮ A new spectral meshless radial point interpolation (SMRPI) method for the two-dimensional Fredholm integral equations on general domains with error analysis ⋮ Error asymptotic expansion for the numerical approximation of logarithmic-kernel integral equations on closed curves ⋮ On the convergence analysis, stability, and implementation of meshless local radial point interpolation on a class of three-dimensional wave equations ⋮ A class of Runge-Kutta methods for nonlinear Volterra integral equations of the second kind with singular kernels ⋮ A meshless discrete collocation method for the numerical solution of singular-logarithmic boundary integral equations utilizing radial basis functions ⋮ A meshless Galerkin scheme for the approximate solution of nonlinear logarithmic boundary integral equations utilizing radial basis functions ⋮ Numerical pricing of American options under two stochastic factor models with jumps using a meshless local Petrov-Galerkin method ⋮ Numerical simulation of reaction-diffusion neural dynamics models and their synchronization/desynchronization: application to epileptic seizures ⋮ A meshless local discrete Galerkin (MLDG) scheme for numerically solving two-dimensional nonlinear Volterra integral equations ⋮ A numerical scheme for solving a class of logarithmic integral equations arisen from two-dimensional Helmholtz equations using local thin plate splines ⋮ A local Galerkin integral equation method for solving integro-differential equations arising in oscillating magnetic fields ⋮ Multiscale approximation of the solution of weakly singular second kind Fredholm integral equation in Legendre multiwavelet basis ⋮ A new spectral meshless radial point interpolation (SMRPI) method: a well-behaved alternative to the meshless weak forms ⋮ Spectral meshless radial point interpolation (SMRPI) method to two-dimensional fractional telegraph equation ⋮ Thin plate spline Galerkin scheme for numerically solving nonlinear weakly singular Fredholm integral equations ⋮ Pseudospectral Meshless Radial Point Hermit Interpolation Versus Pseudospectral Meshless Radial Point Interpolation ⋮ A MESHLESS LOCAL GALERKIN METHOD FOR THE NUMERICAL SOLUTION OF HAMMERSTEIN INTEGRAL EQUATIONS BASED ON THE MOVING LEAST SQUARES TECHNIQUE

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