Reproducing kernel method for singularly perturbed one-dimensional initial-boundary value problems with exponential initial layers

DOI10.1007/s12346-017-0242-3zbMath1448.65079OpenAlexW2615030674WikidataQ115601506 ScholiaQ115601506MaRDI QIDQ1641845

Fazhan Geng, Zhiqiang Tang, YongFang Zhou

Publication date: 20 June 2018

Published in: Qualitative Theory of Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s12346-017-0242-3

zbMATH Keywords

initial-boundary value problemssingularly perturbed problemsreproducing kernel methodsexponential initial layers

Mathematics Subject Classification ID

Numerical solution of singularly perturbed problems involving ordinary differential equations (65L11) Numerical methods for functional-differential equations (65L03)

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Cites Work

• Unnamed Item
• Piecewise shooting reproducing kernel method for linear singularly perturbed boundary value problems
• A novel method for solving a class of singularly perturbed boundary value problems based on reproducing kernel method
• An efficient numerical scheme for 1D parabolic singularly perturbed problems with an interior and boundary layers
• Solving a nonlinear system of second order boundary value problems
• Numerical solutions of singularly perturbed one-dimensional parabolic convection-diffusion problems by the Bessel collocation method
• A uniformly convergent B-spline collocation method on a nonuniform mesh for singularly perturbed one-dimensional time-dependent linear convection-diffusion problem
• On the uniform convergence of a finite difference scheme for time dependent singularly perturbed reaction-diffusion problems
• An exponentially-fitted method for singularly perturbed, one-dimensional, parabolic problems
• A uniformly convergent scheme on a nonuniform mesh for convection-diffusion parabolic problems
• Another uniform convergence analysis technique of some numerical methods for parabolic singularly perturbed problems
• A numerical method for singularly perturbed turning point problems with an interior layer
• Modified reproducing kernel method for singularly perturbed boundary value problems with a delay
• Reproducing kernel method for singularly perturbed turning point problems having twin boundary layers
• Piecewise reproducing kernel method for singularly perturbed delay initial value problems
• Solving singular two-point boundary value problem in reproducing kernel space
• A higher order uniformly convergent method with Richardson extrapolation in time for singularly perturbed reaction-diffusion parabolic problems
• A computational method for solving third-order singularly perturbed boundary-value problems
• Robust numerical scheme for singularly perturbed convection-diffusion parabolic initial-boundary-value problems on equidistributed grids
• A parameter-uniform numerical method for a Sobolev problem with initial layer
• Theory of Reproducing Kernels