Chebyshev reproducing kernel method: application to two-point boundary value problems

DOI10.1186/s13662-017-1089-2zbMath1422.34104OpenAlexW2581068905WikidataQ59481056 ScholiaQ59481056MaRDI QIDQ1628462

M. Khaleghi, Saeid Abbasbandy, Esmail Babolian

Publication date: 4 December 2018

Published in: Advances in Difference Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1186/s13662-017-1089-2

zbMATH Keywords

convergenceChebyshev polynomialserror estimationDirichlet boundary conditionstwo-point boundary value problempolynomial reproducing kernel

Mathematics Subject Classification ID

Best approximation, Chebyshev systems (41A50) Stability and convergence of numerical methods for ordinary differential equations (65L20) Error bounds for numerical methods for ordinary differential equations (65L70) Nonlocal and multipoint boundary value problems for ordinary differential equations (34B10)

Related Items (9)

An effective approach for numerical solution of linear and nonlinear singular boundary value problems ⋮ A spectral method for the solution of boundary value problems ⋮ Using reproducing kernel for solving a class of fractional order integral differential equations ⋮ Numerical solution of fractional Bratu type equations with Legendre reproducing kernel method ⋮ GENERALIZED JACOBI REPRODUCING KERNEL METHOD IN HILBERT SPACES FOR SOLVING THE BLACK-SCHOLES OPTION PRICING PROBLEM ARISING IN FINANCIAL MODELLING ⋮ Laguerre reproducing kernel method in Hilbert spaces for unsteady stagnation point flow over a stretching/shrinking sheet ⋮ Solving a class of singular two-point boundary value problems using new effective reproducing kernel technique ⋮ A fast numerical method for fractional partial differential equations ⋮ Reproducing kernel method in Hilbert spaces for solving the linear and nonlinear four-point boundary value problems

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Numerical algorithm for solving two-point, second-order periodic boundary value problems for mixed integro-differential equations
• Approximate solutions to three-point boundary value problems with two-space integral condition for parabolic equations
• A numerical solution to nonlinear second order three-point boundary value problems in the reproducing kernel space
• A computational method for two-point boundary value problems of fourth-order mixed integrodifferential equations
• Homotopy perturbation technique for solving two-point boundary value problems -- comparison with other methods
• Solving the generalized regularized long wave equation on the basis of a reproducing kernel space
• Two-point boundary value problems by the extended Adomian decomposition method
• Solving singular second order three-point boundary value problems using reproducing kernel Hilbert space method
• Application of reproducing kernel algorithm for solving second-order, two-point fuzzy boundary value problems
• Numerical investigations for systems of second-order periodic boundary value problems using reproducing kernel method
• A new generalized Jacobi Galerkin operational matrix of derivatives: two algorithms for solving fourth-order boundary value problems
• Error estimation for the reproducing kernel method to solve linear boundary value problems
• New wavelets collocation method for solving second-order multipoint boundary value problems using Chebyshev polynomials of third and fourth kinds
• A novel approach to calculation of reproducing kernel on infinite interval and applications to boundary value problems
• B-spline interpolation compared with finite difference, finite element and finite volume methods which applied to two-point boundary value problems
• The explicit formulas for reproducing kernel of some Hilbert spaces
• Numerical solution of nonlinear three-point boundary value problem on the positive half-line
• On Solving Linear and Nonlinear Sixth-Order Two PointBoundary Value Problems Via an Elegant HarmonicNumbers Operational Matrix of Derivatives
• Exponential Fitting for the Solution of Two-Point Boundary Value Problems with Cubic Spline Collocation Tau-Method
• An elegant operational matrix based on harmonic numbers: Effective solutions for linear and nonlinear fourth-order two point boundary value problems
• Best approximation in inner product spaces

This page was built for publication: Chebyshev reproducing kernel method: application to two-point boundary value problems