A reproducing kernel Hilbert space approach in meshless collocation method

DOI10.1007/s40314-019-0838-0zbMath1438.65245arXiv1705.01364OpenAlexW2962991655MaRDI QIDQ2322462

Babak Azarnavid, Mahdi Emamjome, Mohammad Nabati, Saeid Abbasbandy

Publication date: 4 September 2019

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

Full work available at URL: https://arxiv.org/abs/1705.01364

zbMATH Keywords

collocation methodreproducing kernel Hilbert spacemeshless methodcardinal functionsdifferentiation matrix

Mathematics Subject Classification ID

Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) Nonlinear boundary value problems for ordinary differential equations (34B15) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) Numerical solution of boundary value problems involving ordinary differential equations (65L10) Error bounds for numerical methods for ordinary differential equations (65L70)

Related Items

An efficient kernel-based method for solving nonlinear generalized Benjamin-Bona-Mahony-Burgers equation in irregular domains ⋮ A new structure to \(n\)-dimensional trigonometric cubic B-spline functions for solving \(n\)-dimensional partial differential equations ⋮ The Bernoulli polynomials reproducing kernel method for nonlinear Volterra integro-differential equations of fractional order with convergence analysis ⋮ Numerical solution of second-order two-dimensional hyperbolic equation by bi-cubic B-spline collocation method ⋮ A new application of the reproducing kernel method

Cites Work

• Unnamed Item
• Unnamed Item
• Numerical solutions of nonlinear Burgers equation with modified cubic B-splines collocation method
• A shooting reproducing kernel Hilbert space method for multiple solutions of nonlinear boundary value problems
• Fitted reproducing kernel Hilbert space method for the solutions of some certain classes of time-fractional partial differential equations subject to initial and Neumann boundary conditions
• Some error estimates for the reproducing kernel Hilbert spaces method
• Lattice Boltzmann model for the modified Burgers' equation
• An efficient computational method for linear fifth-order two-point boundary value problems
• Numerical solution of Burgers' equation by cubic B-spline quasi-interpolation
• A comparison of efficiency and error convergence of multiquadric collocation method and finite element method.
• Meshless methods based on collocation with radial basis functions
• A comparison analysis between unsymmetric and symmetric radial basis function collocation methods for the numerical solution of partial differential equations
• Numerical solutions of fractional differential equations of Lane-Emden type by an accurate technique
• On solutions of fractional Riccati differential equations
• New reproducing kernel functions
• Numerical investigations for systems of second-order periodic boundary value problems using reproducing kernel method
• Rhythm oscillation in fractional-order relaxation oscillator and its application in image enhancement
• The numerical solution of fifth-order boundary value problems with sixth-degree B-spline functions
• On unsymmetric collocation by radial basis functions
• Explicit solution of telegraph equation based on reproducing kernel method
• An iterative kernel based method for fourth order nonlinear equation with nonlinear boundary condition
• Nonpolynomial sextic spline method for the solution along with convergence of linear special case fifth-order two-point boundary value problems
• An iterative reproducing kernel method in Hilbert space for the multi-point boundary value problems
• A numerical scheme based on weighted average differential quadrature method for the numerical solution of Burgers' equation
• A meshfree method for the solution of two-dimensional cubic nonlinear Schrödinger equation
• Numerical solution of Burgers' equation by lattice Boltzmann method
• Sextic spline solutions of fifth order boundary value problems
• A numerical solution of the Burgers' equation using septic B-splines
• Assessment of global and local meshless methods based on collocation with radial basis functions for parabolic partial differential equations in three dimensions
• The reproducing kernel algorithm for handling differential algebraic systems of ordinary differential equations
• Approximate Solutions of DASs with Nonclassical Boundary Conditions using Novel Reproducing Kernel Algorithm
• PICARD-REPRODUCING KERNEL HILBERT SPACE METHOD FOR SOLVING GENERALIZED SINGULAR NONLINEAR LANE-EMDEN TYPE EQUATIONS
• Simulation of Seismic Wave Scattering by Embedded Cavities in an Elastic Half-Plane Using the Novel Singular Boundary Method
• On solutions of variable-order fractional differential equations
• Theory of Reproducing Kernels
• Scattered Data Approximation
• All well-posed problems have uniformly stable and convergent discretizations