Numerical solution of singularly perturbed boundary value problems by improved least squares method

DOI10.1016/j.cam.2017.09.023zbMath1377.65092OpenAlexW2763147825MaRDI QIDQ1678123

Peng Zhang

Publication date: 14 November 2017

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.2017.09.023

zbMATH Keywords

algorithmconvergencenumerical examplesboundary value problemsboundary layerleast squares methodB-splinesinterior layersingular perturbed differential equations

Mathematics Subject Classification ID

Nonlinear boundary value problems for ordinary differential equations (34B15) 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 perturbations for ordinary differential equations (34E15) Numerical solution of singularly perturbed problems involving ordinary differential equations (65L11)

Related Items

Numerical solution of two-point nonlinear boundary value problems via Legendre-Picard iteration method, A REPRODUCING KERNEL METHOD FOR SOLVING SINGULARLY PERTURBED DELAY PARABOLIC PARTIAL DIFFERENTIAL EQUATIONS, Robust preview control for uncertain discrete singular systems, Unnamed Item, The existence and asymptotic estimates of solutions for a third-order nonlinear singularly perturbed boundary value problem, High-order Gegenbauer integral spectral element method integrated with an adaptive Chebyshev optimization strategy for solving linear singularly perturbed differential equations

Uses Software

• RWPM

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A parameter robust higher order numerical method for singularly perturbed two parameter problems with non-smooth data
• Robust a posteriori error bounds for spline collocation applied to singularly perturbed reaction-diffusion problems
• The Lie-group shooting method for solving nonlinear singularly perturbed boundary value problems
• Approximation of singularly perturbed reaction-diffusion problems by quadratic \(C ^1\)-splines
• Richardson extrapolation for a singularly perturbed turning point problem with exponential boundary layers
• B-splines with artificial viscosity for solving singularly perturbed boundary value problems
• Numerical solution of singularly perturbed boundary value problems based on optimal control strategy
• A finite-difference method for a singularly perturbed delay integro-differential equation
• A parameter uniform difference scheme for singularly perturbed parabolic problem in one space dimension
• RWPM: A software package of shooting methods for nonlinear two-point boundary value problems
• A new method for solving singular initial value problems in the second-order ordinary differential equations
• ``Shooting method for the solution of singularly perturbed two-point boundary-value problems having less severe boundary layer.
• A numerical method for singularly perturbed turning point problems with an interior layer
• Optimal B-spline collocation method for self-adjoint singularly perturbed boundary value problems
• Robust approximation of singularly perturbed delay differential equations by the \(hp\) finite element method
• Variable-mesh difference scheme for singularly-perturbed boundary-value problems using splines
• Nonlinear Ordinary Differential Equations
• A collocation method based on the Bessel functions of the first kind for singular perturbated differential equations and residual correction
• Robust Numerical Methods for Singularly Perturbed Differential Equations
• An Adaptive Shooting Method for Singularly Perturbed Boundary Value Problems
• ‘Shooting method' for singular perturbation problems arising in chemical reactor theory
• Layer-adapted meshes for one-dimensional reaction–convection–diffusion problems
• ‘Shooting method’ for singularly perturbed one-dimensional reaction-diffusion neumann problems
• Shooting Methods for Two‐Point BVPs with Partially Separated Endconditions