Comparison of a higher order method and the simple upwind and non-monotone methods for singularly perturbed boundary value problems

DOI10.1016/j.amc.2006.04.007zbMath1106.65066OpenAlexW2088389477MaRDI QIDQ861129

M. Mokarram Shahraki, Mohammed Hosseini Ali Abadi

Publication date: 9 January 2007

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

Full work available at URL: https://doi.org/10.1016/j.amc.2006.04.007

zbMATH Keywords

numerical resultssingular perturbationuniform convergencefinite difference methodsShishkin meshupwind methods

Mathematics Subject Classification ID

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) Mesh generation, refinement, and adaptive methods for ordinary differential equations (65L50)

Related Items (3)

Optimal error estimate using mesh equidistribution technique for singularly perturbed system of reaction-diffusion boundary-value problems ⋮ A brief survey on numerical methods for solving singularly perturbed problems ⋮ Numerical treatment of singularly perturbed two-point boundary value problems by using differential transformation method

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Inadequacy of first-order upwind difference schemes for some recirculating flows
• Numerical methods for time-dependent convection-diffusion equations
• Uniform fourth order difference scheme for a singular perturbation problem
• A fractional step method on a special mesh for the resolution of multidimensional evolutionary convection-diffusion problems
• A uniformly convergent scheme on a nonuniform mesh for convection-diffusion parabolic problems
• A priori meshes for singularly perturbed quasilinear two-point boundary value problems
• A Globally Uniformly Convergent Finite Element Method for a Singularly Perturbed Elliptic Problem in Two Dimensions
• Graded-Mesh Difference Schemes for Singularly Perturbed Two-Point Boundary Value Problems
• Uniform High-Order Difference Schemes for a Singularly Perturbed Two-Point Boundary Value Problem
• Asymptotic Analysis of a Singular Perturbation Problem
• Sufficient Conditions for Uniform Convergence of a Class of Difference Schemes for a Singularly Perturbed Problem
• Analysis of Some Difference Approximations for a Singular Perturbation Problem Without Turning Points
• The use of special transformations in the numerical solution of boundary-layer problems

This page was built for publication: Comparison of a higher order method and the simple upwind and non-monotone methods for singularly perturbed boundary value problems