An exponentially fitted special second-order finite difference method for solving singular perturbation problems

DOI10.1016/j.amc.2007.02.051zbMath1122.65377OpenAlexW1999833904MaRDI QIDQ2383929

Andargie Awoke, Y. N. Reddy

Publication date: 19 September 2007

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

Full work available at URL: https://doi.org/10.1016/j.amc.2007.02.051

zbMATH Keywords

stabilitynumerical examplesfinite differencesboundary layertwo-point boundary value problemsexponential fittingThomas algorithmSingular perturbation problemslinear and nonlinear problemsfitted method

Mathematics Subject Classification ID

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) Finite difference and finite volume methods for ordinary differential equations (65L12)

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Boundary shape functions methods for solving the nonlinear singularly perturbed problems with Robin boundary conditions ⋮ A higher order accurate numerical method for singularly perturbed two point boundary value problems ⋮ An optimal asymptotic-numerical method for convection dominated systems having exponential boundary layers ⋮ Wavelets collocation method for singularly perturbed differential-difference equations arising in control system ⋮ The Lie-group shooting method for solving nonlinear singularly perturbed boundary value problems ⋮ An efficient mixed asymptotic-numerical scheme for singularly perturbed convection diffusion problems ⋮ High order multiplication perturbation method for singular perturbation problems ⋮ Analytic approximation to delayed convection dominated systems through transforms ⋮ High-order exponentially fitted difference schemes for singularly perturbed two-point boundary value problems ⋮ Solving second-order singularly perturbed ODE by the collocation method based on energetic Robin boundary functions. ⋮ Solution of singularly perturbed differential difference equations and convection delayed dominated diffusion equations using Haar wavelet ⋮ Modified asymptotic solutions for second-order nonlinear singularly perturbed boundary value problems ⋮ Solving singularly perturbed problems by a weak-form integral equation with exponential trial functions

Cites Work

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• Perturbation methods in applied mathematics
• An exponentially fitted finite difference method for singular perturbation problems
• An initial-value approach for solving singularly perturbed two-point boundary value problems
• Perturbation methods and non-linear hyperbolic waves

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