Second order parameter-uniform convergence for a finite difference method for a singularly perturbed linear reaction-diffusion system

zbMath1223.65062arXiv1004.0681MaRDI QIDQ3069453

S. Valarmathi, M. Paramasivam, John J. H. Miller

Publication date: 26 January 2011

Full work available at URL: https://arxiv.org/abs/1004.0681

zbMATH Keywords

convergencesingular perturbationnumerical examplesShishkin meshsystemreaction-diffusion typeclassical finite difference schemeparameter-uniformoverlapping boundary layers

Mathematics Subject Classification ID

Stability and convergence of numerical methods for ordinary differential equations (65L20) Linear ordinary differential equations and systems (34A30) Numerical solution of boundary value problems involving ordinary differential equations (65L10) Error bounds for numerical methods for ordinary differential equations (65L70) 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) Numerical solution of singularly perturbed problems involving ordinary differential equations (65L11)

Related Items

A parameter robust fitted mesh finite difference method for a system of two reaction-convection-diffusion equations ⋮ A parameter uniform fitted mesh method for a weakly coupled system of two singularly perturbed convection-diffusion equations ⋮ Solving systems of singularly perturbed convection diffusion problems via initial value method ⋮ Unnamed Item ⋮ Numerical treatment for a coupled system of singularly perturbed reaction-diffusion equations with Robin boundary conditions and having boundary and interior layers ⋮ Initial or Boundary Value Problems for Systems of Singularly Perturbed Differential Equations and Their Solution Profile ⋮ Convergence of the Crank-Nicolson Method for a Singularly Perturbed Parabolic Reaction-Diffusion System ⋮ A Parameter-Uniform First Order Convergent Numerical Method for a Semi-linear System of Singularly Perturbed Second Order Delay Differential Equations ⋮ A parameter uniform essentially first-order convergent numerical method for a parabolic system of singularly perturbed differential equations of reaction–diffusion type with initial and Robin boundary conditions ⋮ Unnamed Item ⋮ Numerical Solution to Singularly Perturbed Differential Equation of Reaction-Diffusion Type in MAGDM Problems ⋮ Parameter-uniform convergence of a numerical method for a coupled system of singularly perturbed semilinear reaction-diffusion equations with boundary and interior layers ⋮ A Parameter-Uniform First Order Convergent Numerical Method for a System of Singularly Perturbed Second Order Delay Differential Equations ⋮ Second Order Uniformly Convergent Numerical Method for a Coupled System of Singularly Perturbed Reaction-Diffusion Problems with Discontinuous Source Term ⋮ A parameter-uniform fitted mesh method for a weakly coupled system of three partially singularly perturbed convection-diffusion equations ⋮ A parameter-uniform essentially first-order convergence of a fitted mesh method for a class of parabolic singularly perturbed system of Robin problems ⋮ Fitted mesh methods for a class of weakly coupled system of singularly perturbed convection-diffusion equations