The series expansion and Chebyshev collocation method for nonlinear singular two-point boundary value problems

DOI10.1007/s10665-020-10077-0zbMath1476.65147OpenAlexW3122055921MaRDI QIDQ2060958

Tongke Wang, Yiting Kong, Zhi-Fang Liu

Publication date: 13 December 2021

Published in: Journal of Engineering Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10665-020-10077-0

zbMATH Keywords

convergence analysisGreen's functionEmden-Fowler equationChebyshev collocation methodThomas-Fermi equationnonlinear singular two-point boundary value problemfractional series expansion

Mathematics Subject Classification ID

Stability and convergence of numerical methods for ordinary differential equations (65L20) Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations (65L60) Numerical solution of boundary value problems involving ordinary differential equations (65L10) Singular nonlinear boundary value problems for ordinary differential equations (34B16) Linear boundary value problems for ordinary differential equations (34B05)

Related Items (3)

Series solution and Chebyshev collocation method for the initial value problem of Emden-Fowler equation ⋮ Singular asymptotic expansion and Legendre collocation method for two-term weakly singular Volterra integral equation of the second kind ⋮ Singularity separation Chebyshev collocation method for weakly singular Volterra integral equations of the second kind

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• An efficient numerical technique for the solution of nonlinear singular boundary value problems
• The estimation of truncation error by \(\tau\)-estimation for Chebyshev spectral collocation method
• A novel approach for the solution of a class of singular boundary value problems arising in physiology
• A uniform mesh finite difference method for a class of singular two-point boundary value problems
• Numerical study for a class of singular two-point boundary value problems using Green's functions
• A novel numerical approach and its convergence for numerical solution of nonlinear doubly singular boundary value problems
• Implementation of new iterative techniques for solutions of Thomas-Fermi and Emden-Fowler equations
• Finite difference methods and their convergence for a class of singular two point boundary value problems
• Singular boundary-value problems for ordinary second-order differential equations
• A numerical method for singular two point boundary value problems via Chebyshev eco\-no\-mi\-zi\-tion.
• A new high-order numerical method for solving singular two-point boundary value problems
• Accurate calculation of the solutions to the Thomas-Fermi equations
• Numerical solution of singular two-point boundary value problems by the collocation method with the Chebyshev bases
• On singular BVPs with nonsmooth data: convergence of the collocation schemes
• An algorithm for the inversion of Laplace transforms using Puiseux expansions
• Numerical solution of singular boundary value problems via Chebyshev polynomial and B-spline
• A fourth-order finite difference method based on uniform mesh for singular two-point boundary-value problems
• A modified spectral method for numerical solution of ordinary differential equations with non-analytic solution
• A compact finite difference method for a general class of nonlinear singular boundary value problems with Neumann and Robin boundary conditions
• The Thomas-Fermi problem and solutions of the Emden-Fowler equation
• The practical Gauss type rules for Hadamard finite-part integrals using Puiseux expansions
• A new numerical approach for solving a class of singular two-point boundary value problems
• Numerical solution of singular boundary value problems using Green's function and improved decomposition method
• On the convergence of finite-difference approximations to one-dimensional singular boundary-value problems
• Some aspects of the Thomas-Fermi equation
• Numerical methods of high-order accuracy for singular nonlinear boundary value problems
• A numerical method for solving singular boundary value problems
• A hybrid asymptotic and augmented compact finite volume method for nonlinear singular two point boundary value problems
• The modified composite Gauss type rules for singular integrals using Puiseux expansions
• Chebyshev Spectral Methods and the Lane-Emden Problem
• Spectral Methods
• Numerical Methods for Singular Boundary Value Problems
• Galerkin Methods for Singular Boundary Value Problems in One Space Dimension
• Finite Difference Methods for Singular Two-Point Boundary Value Problems
• A Uniform Mesh Finite Difference Method for a Class of Singular Two-Point Boundary Value Problems
• Finite Element Methods of High-Order Accuracy for Singular Two-Point Boundary Value Problems with Nonsmooth Solutions
• On the Generalized Emden–Fowler Equation
• Collocation Methods for Singular Boundary Value Problems
• A finite-difference method for the spectral approximation of a class of singular two-point boundary value problems
• On a finite difference method for singular two-point boundary value problems
• Convergence Analysis of Spectral Collocation Methods for a Singular Differential Equation
• A new highly accurate domain decomposition optimal homotopy analysis method and its convergence for singular boundary value problems
• A fast and accurate computational technique for efficient numerical solution of nonlinear singular boundary value problems
• The asymptotic expansion and extrapolation of trapezoidal rule for integrals with fractional order singularities
• A Local Fractional Taylor Expansion and Its Computation for Insufficiently Smooth Functions
• ON THE THOMAS-FERMI EQUATION
• Analysis of a New Error Estimate for Collocation Methods Applied to Singular Boundary Value Problems
• Correction method and extrapolation method for singular two-point boundary value problems
• Jacobi interpolation approximations and their applications to singular differential equations

This page was built for publication: The series expansion and Chebyshev collocation method for nonlinear singular two-point boundary value problems