Error estimation for the reproducing kernel method to solve linear boundary value problems
From MaRDI portal
Publication:1936183
DOI10.1016/j.cam.2012.11.002zbMath1261.65085OpenAlexW2043848760MaRDI QIDQ1936183
Publication date: 21 February 2013
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.2012.11.002
numerical exampleserror estimationreproducing kernel methodlinear second order two-point boundary value problem
Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces) (46E22) Numerical solution of boundary value problems involving ordinary differential equations (65L10) Error bounds for numerical methods for ordinary differential equations (65L70) Linear boundary value problems for ordinary differential equations (34B05)
Related Items (62)
Numerical solution for a class of space-time fractional equation by the piecewise reproducing kernel method ⋮ A new numerical method for singularly perturbed turning point problems with two boundary layers based on reproducing kernel method ⋮ A new reproducing kernel method for Duffing equations ⋮ Approximate solutions of Atangana-Baleanu variable order fractional problems ⋮ Chebyshev reproducing kernel method: application to two-point boundary value problems ⋮ A new reproducing kernel method for linear nonlocal boundary value problems ⋮ Improved reproducing kernel method for singularly perturbed differential-difference equations with boundary layer behavior ⋮ Using the iterative reproducing kernel method for solving a class of nonlinear fractional differential equations ⋮ Piecewise shooting reproducing kernel method for linear singularly perturbed boundary value problems ⋮ Solving the Dym initial value problem in reproducing kernel space ⋮ A posteriori analysis: error estimation for the eighth order boundary value problems in reproducing kernel space ⋮ On accuracy and stability analysis of the reproducing kernel space method for the forced Duffing equation ⋮ A continuous kernel functions method for mixed-type functional differential equations ⋮ A new reproducing kernel-based collocation method with optimal convergence rate for some classes of BVPs ⋮ An attractive numerical algorithm for solving nonlinear Caputo-Fabrizio fractional Abel differential equation in a Hilbert space ⋮ A unified reproducing kernel method and error estimation for solving linear differential equation with functional constraints ⋮ Reproducing kernel method for solving singularly perturbed differential-difference equations with boundary layer behavior in Hilbert space ⋮ Fuzzy reproducing kernel space method for solving fuzzy boundary value problems ⋮ A new kernel functions based approach for solving 1-D interface problems ⋮ Mixed reproducing kernel-based iterative approach for nonlinear boundary value problems with nonlocal conditions ⋮ A new higher order accurate reproducing kernel-based approach for boundary value problems ⋮ A new reproducing kernel method with higher convergence order for solving a Volterra-Fredholm integral equation ⋮ A generalized collocation method in reproducing kernel space for solving a weakly singular Fredholm integro-differential equations ⋮ A new multiscale algorithm for solving second order boundary value problems ⋮ A novel method with error analysis for the numerical solution of a logarithmic singular Fredholm integral equation ⋮ An optimal reproducing kernel method for linear nonlocal boundary value problems ⋮ A stable least residue method in reproducing kernel space for solving a nonlinear fractional integro-differential equation with a weakly singular kernel ⋮ An efficient numerical algorithm for solving nonlinear fractional Volterra integro-differential equation ⋮ Some error estimates for the reproducing kernel Hilbert spaces method ⋮ A numerical method for solving distributed order diffusion equations ⋮ A hybrid kernel functions collocation approach for boundary value problems with Caputo fractional derivative ⋮ An effective approach for numerical solution of linear and nonlinear singular boundary value problems ⋮ An accurate numerical technique for fractional oscillation equations with oscillatory solutions ⋮ Reproducing kernel method to solve non-local fractional boundary value problem ⋮ A new reproducing kernel collocation method for nonlocal fractional boundary value problems with non-smooth solutions ⋮ Fitted reproducing kernel method for singularly perturbed delay initial value problems ⋮ Solutions of integral equations by reproducing kernel Hilbert space method ⋮ Reproducing kernel function-based Filon and Levin methods for solving highly oscillatory integral ⋮ Using reproducing kernel for solving a class of fractional order integral differential equations ⋮ A new numerical method for variable order fractional functional differential equations ⋮ A numerical method for singularly perturbed turning point problems with an interior layer ⋮ Reproducing kernel method for the numerical solution of the 1D Swift-Hohenberg equation ⋮ Piecewise reproducing kernel method for linear impulsive delay differential equations with piecewise constant arguments ⋮ Stability and error analysis of the reproducing kernel Hilbert space method for the solution of weakly singular Volterra integral equation on graded mesh ⋮ Computational method based on reproducing kernel for solving singularly perturbed differential-difference equations with a delay ⋮ Modified reproducing kernel method for singularly perturbed boundary value problems with a delay ⋮ Some error estimates for solving Volterra integral equations by using the reproducing kernel method ⋮ Reproducing kernel method for the numerical solution of the Brinkman-Forchheimer momentum equation ⋮ A new reproducing kernel method for variable order fractional boundary value problems for functional differential equations ⋮ Error analysis of reproducing kernel Hilbert space method for solving functional integral equations ⋮ Solving system of second-order BVPs using a new algorithm based on reproducing kernel Hilbert space ⋮ Soft computing technique for a system of fuzzy Volterra integro-differential equations in a Hilbert space ⋮ A Novel Method for Nonlinear Boundary Value Problems Based on Multiscale Orthogonal Base ⋮ A stable and efficient technique for linear boundary value problems by applying kernel functions ⋮ A reproducing kernel method for nonlinear C-q-fractional IVPs ⋮ Unnamed Item ⋮ Reproducing kernel method for singularly perturbed turning point problems having twin boundary layers ⋮ A numerical technique for variable fractional functional boundary value problems ⋮ A new piecewise reproducing kernel function algorithm for solving nonlinear Hamiltonian systems ⋮ Piecewise reproducing kernel method for singularly perturbed delay initial value problems ⋮ Iterative reproducing kernel method for nonlinear variable-order space fractional diffusion equations ⋮ Reproducing kernel method in Hilbert spaces for solving the linear and nonlinear four-point boundary value problems
This page was built for publication: Error estimation for the reproducing kernel method to solve linear boundary value problems
