Parameter-uniform numerical method for global solution and global normalized flux of singularly perturbed boundary value problems using grid equidistribution

DOI10.1016/j.camwa.2010.07.026zbMath1205.65221OpenAlexW2010018027MaRDI QIDQ623117

Srinivasan Natesan, Jugal Mohapatra

Publication date: 13 February 2011

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.camwa.2010.07.026

zbMATH Keywords

uniform convergenceupwind schemeadaptive meshsingularly perturbed convection-diffusion problemsnormalized flux

Mathematics Subject Classification ID

Finite difference and finite volume methods for ordinary differential equations (65L12) Numerical solution of singularly perturbed problems involving ordinary differential equations (65L11)

Related Items (14)

Parameter-uniform numerical methods for a class of parameterized singular perturbation problems ⋮ Parameter-uniform hybrid difference scheme for solutions and derivatives in singularly perturbed initial value problems ⋮ An efficient adaptive grid method for a system of singularly perturbed convection-diffusion problems with Robin boundary conditions ⋮ A fast uniformly accurate global numerical approximation to solution and scaled derivative of system of singularly perturbed problems with multiple diffusion parameters on generalized adaptive mesh ⋮ Numerical analysis of a system of semilinear singularly perturbed first‐order differential equations on an adaptive grid ⋮ A second-order adaptive grid method for a nonlinear singularly perturbed problem with an integral boundary condition ⋮ An initial value method for solving singularly perturbed boundary value problems using adaptive grids ⋮ Parameter-uniform numerical methods for singularly perturbed mixed boundary value problems using grid equidistribution ⋮ A robust numerical approach for singularly perturbed third order boundary value problem on layer adapted meshes ⋮ Uniformly convergent hybrid schemes for solutions and derivatives in quasilinear singularly perturbed BVPs ⋮ A robust adaptive grid method for a nonlinear singularly perturbed differential equation with integral boundary condition ⋮ A moving mesh refinement based optimal accurate uniformly convergent computational method for a parabolic system of boundary layer originated reaction-diffusion problems with arbitrary small diffusion terms ⋮ Convergence analysis of a finite difference scheme for a Riemann-Liouville fractional derivative two-point boundary value problem on an adaptive grid ⋮ A recent development of computer methods for solving singularly perturbed boundary value problems

Cites Work

• Higher order global solution and normalized flux for singularly perturbed reaction-diffusion problems
• Convergence analysis of finite difference approximations on equidistributed grids to a singularly perturbed boundary value problem
• Numerical solution of a singularly perturbed two-point boundary value problem using equidistribution: Analysis of convergence
• Uniform convergence analysis of finite difference approximations for singular perturbation problems on an adapted grid
• Uniform Convergence Analysis of Finite Difference Scheme for Singularly Perturbed Delay Differential Equation on an Adaptively Generated Grid
• A robust second-order numerical method for global solution and global normalized flux of singularly perturbed self-adjoint boundary-value problems
• On the Approximation of Derivatives of Singularly Perturbed Boundary Value Problems
• Analysis of Some Difference Approximations for a Singular Perturbation Problem Without Turning Points
• Uniform convergence analysis of an upwind finite-difference approximation of a convection-diffusion boundary value problem on an adaptive grid
• Approximation of derivatives in a convection-diffusion two-point boundary value problem
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