Kudu, Mustafa; Amirali, Ilhame; Amiraliyev, Gabil M. Uniform numerical approximation for parameter dependent singularly perturbed problem with integral boundary condition. (English) Zbl 1463.65202 Miskolc Math. Notes 19, No. 1, 337-353 (2018). Summary: In this paper, a parameter-uniform numerical method for a parameterized singularly perturbed ordinary differential equation containing integral boundary condition is studied. Asymptotic estimates on the solution and its derivatives are derived. A numerical algorithm based on upwind finite difference operator and an appropriate piecewise uniform mesh is constructed. Parameter-uniform error estimate for the numerical solution is established. Numerical results are presented, which illustrate the theoretical results. Cited in 6 Documents MSC: 65L11 Numerical solution of singularly perturbed problems involving ordinary differential equations 65L12 Finite difference and finite volume methods for ordinary differential equations 65L20 Stability and convergence of numerical methods for ordinary differential equations 65L70 Error bounds for numerical methods for ordinary differential equations Keywords:parameterized problem; singular perturbation; uniform convergence; finite difference scheme; Shiskin mesh; integral boundary condition PDFBibTeX XMLCite \textit{M. Kudu} et al., Miskolc Math. Notes 19, No. 1, 337--353 (2018; Zbl 1463.65202) Full Text: DOI