A finite difference method for the singularly perturbed problem with nonlocal boundary condition

DOI10.1016/j.amc.2003.11.035zbMath1068.65100OpenAlexW2071375343MaRDI QIDQ706781

D. Kharzeev

Publication date: 9 February 2005

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

Full work available at URL: https://doi.org/10.1016/j.amc.2003.11.035

zbMATH Keywords

numerical examplesingular perturbationuniform convergencefinite difference schemeboundary value problemboundary layernonlocal boundary conditionexponential fittingexponential basis functionsinterpolating quadrature rulesmethod of integral identities

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)

Related Items (30)

Parameter-uniform numerical scheme for singularly perturbed delay parabolic reaction diffusion equations with integral boundary condition ⋮ A second order numerical method for singularly perturbed problem with non-local boundary condition ⋮ Internal layer solution of singularly perturbed optimal control problem with integral boundary condition ⋮ ROBUST NUMERICAL METHOD FOR SINGULARLY PERTURBED CONVECTION-DIFFUSION TYPE PROBLEMS WITH NON-LOCAL BOUNDARY CONDITION ⋮ Solving a singular beam equation by the method of energy boundary functions ⋮ Exponential fitted operator method for singularly perturbed convection-diffusion type problems with nonlocal boundary condition ⋮ A brief survey on numerical methods for solving singularly perturbed problems ⋮ On the uniqueness of linear convection-diffusion equations with integral boundary conditions ⋮ A non-uniform Haar wavelet method for a singularly perturbed convection-diffusion type problem with integral boundary condition on an exponentially graded mesh ⋮ Uniqueness and asymptotics of singularly perturbed equations involving implicit boundary conditions ⋮ NUMERICAL METHOD FOR A SYSTEM OF SINGULARLY PERTURBED CONVECTION DIFFUSION EQUATIONS WITH INTEGRAL BOUNDARY CONDITIONS ⋮ Unnamed Item ⋮ A new numerical approach for a singularly perturbed problem with two integral boundary conditions ⋮ Unnamed Item ⋮ Numerical method for a system of singularly perturbed reaction diffusion equations with integral boundary conditions ⋮ Parameter uniform method for a singularly perturbed system of delay differential equations of reaction-diffusion type with integral boundary conditions ⋮ A recent survey on computational techniques for solving singularly perturbed boundary value problems ⋮ Solving the forced Duffing equation with integral boundary conditions in the reproducing kernel space ⋮ Accelerated exponentially fitted operator method for singularly perturbed problems with integral boundary condition ⋮ New method based on the HPM and RKHSM for solving forced Duffing equations with integral boundary conditions ⋮ A robust adaptive grid method for a nonlinear singularly perturbed differential equation with integral boundary condition ⋮ A boundary value approach for a class of linear singularly perturbed boundary value problems ⋮ A parameter-uniform collocation scheme for singularly perturbed delay problems with integral boundary condition ⋮ Fitted finite difference method for third order singularly perturbed convection diffusion equations with integral boundary condition ⋮ Singularly perturbed delay differential equations of convection-diffusion type with integral boundary condition ⋮ The difference schemes for solving singularly perturbed three-point boundary value problem ⋮ Second order singularly perturbed delay differential equations with non-local boundary condition ⋮ A hybrid numerical scheme for singular perturbation delay problems with integral boundary condition ⋮ Unnamed Item ⋮ A NUMERICAL STUDY ON THE DIFFERENCE SOLUTION OF SINGULARLY PERTURBED SEMILINEAR PROBLEM WITH INTEGRAL BOUNDARY CONDITION

Cites Work

• Singular perturbation methods for ordinary differential equations
• A survey of numerical techniques for solving singularly perturbed ordinary differential equations
• Numerical solution of the singularly perturbed problem with nonlocal boundary condition
• Perturbation methods and non-linear hyperbolic waves
• Numerical solutions of reaction-diffusion equations with nonlocal boundary conditions
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: A finite difference method for the singularly perturbed problem with nonlocal boundary condition