Quintic B-spline method for solving second order linear and nonlinear singularly perturbed two-point boundary value problems

DOI10.1016/j.cam.2017.01.011zbMath1360.65198OpenAlexW2573171964MaRDI QIDQ515764

Ram Kishun Lodhi, Hradyesh Kumar Mishra

Publication date: 16 March 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.2017.01.011

zbMATH Keywords

uniform convergencenonlinearquasilinearizationboundary layerslinearShishkin meshnumerical resultsingularly perturbed boundary value problemsquintic B-spline method

Mathematics Subject Classification ID

Numerical computation using splines (65D07) Nonlinear boundary value problems for ordinary differential equations (34B15) Stability and convergence of numerical methods for ordinary differential equations (65L20) Numerical solution of boundary value problems involving ordinary differential equations (65L10) Linear boundary value problems for ordinary differential equations (34B05) Singular perturbations for ordinary differential equations (34E15) Numerical solution of singularly perturbed problems involving ordinary differential equations (65L11)

Related Items (11)

The existence, uniqueness and asymptotic estimates of solutions for third-order full nonlinear singularly perturbed vector boundary value problems ⋮ A new tension B-spline method for third-order self-adjoint singularly perturbed boundary value problems ⋮ Unnamed Item ⋮ Wavelet multiresolution interpolation Galerkin method for nonlinear boundary value problems with localized steep gradients ⋮ Solution of dual boundary layer singular perturbation problem by septic Hermite collocation technique ⋮ A new implicit-explicit local differential method for boundary value problems ⋮ A quadratic B-spline collocation method for a singularly perturbed semilinear reaction-diffusion problem with discontinuous source term ⋮ A modified graded mesh and higher order finite element approximation for singular perturbation problems ⋮ Quintic B-spline method for solving second order linear and nonlinear singularly perturbed two-point boundary value problems ⋮ The existence and asymptotic estimates of solutions for a third-order nonlinear singularly perturbed boundary value problem ⋮ On the error estimation of spline method for second order boundary value problem

Cites Work

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• Numerical study of singularly perturbed differential-difference equation arising in the modeling of neuronal variability
• Numerical analysis of singularly perturbed delay differential turning point problem
• A novel method for solving a class of singularly perturbed boundary value problems based on reproducing kernel method
• A numerical method for a nonlinear singularly perturbed interior layer problem using an approximate layer location
• Quintic B-spline method for solving second order linear and nonlinear singularly perturbed two-point boundary value problems
• Collocation method using artificial viscosity for solving stiff singularly perturbed turning point problem having twin boundary layers
• B-splines with artificial viscosity for solving singularly perturbed boundary value problems
• A parallel boundary value technique for singularly perturbed two-point boundary value problems
• A boundary value approach for a class of linear singularly perturbed boundary value problems
• Numerical solution of singularly perturbed convection-diffusion problem using parameter uniform B-spline collocation method
• Numerical treatment of singularly perturbed two point boundary value problems using initial-value method
• Parameter uniform numerical method for singularly perturbed turning point problems exhibiting boundary layers.
• A numerical algorithm for singular perturbation problems exhibiting weak boundary layers.
• An initial-value approach for solving singularly perturbed two-point boundary value problems
• A computational method for singularly perturbed nonlinear differential-difference equations with small shift
• Numerical solution of nonlinear singularly perturbed problems on nonuniform meshes by using a non-standard algorithm
• A numerical method for singularly perturbed turning point problems with an interior layer
• Existence and asymptotic stability of periodic solutions with an interior layer of reaction-advection-diffusion equations
• An adaptive mesh strategy for singularly perturbed convection diffusion problems
• B-spline collocation method for nonlinear singularly-perturbed two-point boundary-value problems
• An efficient numerical method for singular perturbation problems
• Comparative study of singularly perturbed two-point BVPs via: Fitted-mesh finite difference method, B-spline collocation method and finite element method
• On error bounds for spline interpolation
• Numerical Solution of Singularly Perturbed Non-Linear Two Point Boundary Value Problems by Spline in Compression
• Error expansion for a first-order upwind difference scheme applied to a model convection-diffusion problem
• NUMERICAL SOLUTION OF A CLASS OF NONLINEAR SYSTEM OF SECOND-ORDER BOUNDARY-VALUE PROBLEMS: A FOURTH-ORDER CUBIC SPLINE APPROACH
• An Initial-Value Technique for Singularly Perturbed Boundary Value Problems via Cubic Spline

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