A new method for solving singular fourth-order boundary value problems with mixed boundary conditions

DOI10.1016/j.amc.2011.02.002zbMath1221.65177OpenAlexW2070484554MaRDI QIDQ535414

Xiaona Li, Xuejun Cao, Yu-Lan Wang

Publication date: 11 May 2011

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

Full work available at URL: https://doi.org/10.1016/j.amc.2011.02.002

zbMATH Keywords

collocation methoderror estimationmixed boundary value problemsreproducing kernel Hilbert spacefourth orderGram-Schmidt orthonormalizationsingular-coefficient

Mathematics Subject Classification ID

Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations (65L60) 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 (20)

Numerical solution for a class of space-time fractional equation by the piecewise reproducing kernel method ⋮ An efficient computational method for a class of singularly perturbed delay parabolic partial differential equation ⋮ Using the iterative reproducing kernel method for solving a class of nonlinear fractional differential equations ⋮ Solving the Dym initial value problem in reproducing kernel space ⋮ Solving a class of linear nonlocal boundary value problems using the reproducing kernel ⋮ Using reproducing kernel for solving a class of fractional partial differential equation with non-classical conditions ⋮ Reproducing kernel method for solving singularly perturbed differential-difference equations with boundary layer behavior in Hilbert space ⋮ Numerical solution of a class of time-fractional order diffusion equations in a new reproducing kernel space ⋮ Reproducing kernel method to solve parabolic partial differential equations with nonlocal conditions ⋮ Reproducing kernel method to solve non-local fractional boundary value problem ⋮ The solution of a class of singularly perturbed two-point boundary value problems by the iterative reproducing kernel method ⋮ Solving a class of singularly perturbed partial differential equation by using the perturbation method and reproducing kernel method ⋮ Using an effective numerical method for solving a class of Lane-Emden equations ⋮ The solution of nonlinear fourth-order differential equation with integral boundary conditions ⋮ A continuous method for nonlocal functional differential equations with delayed or advanced arguments ⋮ Reproducing kernel method for the numerical solution of the 1D Swift-Hohenberg equation ⋮ Computational method based on reproducing kernel for solving singularly perturbed differential-difference equations with a delay ⋮ Reproducing kernel method for the numerical solution of the Brinkman-Forchheimer momentum equation ⋮ Solving a class of singular fifth-order boundary value problems using reproducing kernel Hilbert space method ⋮ Using reproducing kernel for solving a class of time-fractional telegraph equation with initial value conditions

Cites Work

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• Symmetric positive solutions for \(p\)-Laplacian fourth-order differential equations with integral boundary conditions
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• New algorithm for second-order boundary value problems of integro-differential equation
• A three point boundary value problem for nonlinear fourth order differential equations.
• On multi-point boundary value problems for linear ordinary differential equations with singularities
• Solving singular boundary-value problems of higher even-order
• A new method for solving a class of singular two-point boundary value problems
• Existence results for a fourth-order ordinary differential equation with a four-point boundary condition
• Existence of solutions for fourth order differential equation with four-point boundary conditions
• Existence and uniqueness theorems for the bending of an elastic beam equation

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