A Shishkin mesh for a singularly perturbed Riccati equation

DOI10.1016/j.cam.2004.12.018zbMath1079.65088OpenAlexW1710534929MaRDI QIDQ557775

Jianyong Qiao, Sumit K. Garg

Publication date: 30 June 2005

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

Full work available at URL: https://doi.org/10.1016/j.cam.2004.12.018

zbMATH Keywords

error boundsinitial value problemShishkin meshRiccati equationSingular perturbation

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Numerical methods for initial value problems involving ordinary differential equations (65L05) Error bounds for numerical methods for ordinary differential equations (65L70) Singular perturbations for ordinary differential equations (34E15) Mesh generation, refinement, and adaptive methods for ordinary differential equations (65L50)

Related Items (8)

An exponential convergence approximation to singularly perturbed problems by log orthogonal functions ⋮ A brief survey on numerical methods for solving singularly perturbed problems ⋮ Parameter-uniform numerical methods for some linear and nonlinear singularly perturbed convection diffusion boundary turning point problems ⋮ Numerical solution of nonlinear singularly perturbed problems on nonuniform meshes by using a non-standard algorithm ⋮ Numerical solution of nonlinear singularly perturbed problems by using a non-standard algorithm on variable stepsize implementation (CMMSE-2009) ⋮ A numerical method for a nonlinear singularly perturbed interior layer problem using an approximate layer location ⋮ Parameter-uniform numerical methods for some singularly perturbed nonlinear initial value problems ⋮ On the hybrid finite difference scheme for a singularly perturbed Riccati equation

Cites Work

• A uniform scheme for the singularly perturbed Riccati equation
• Singular perturbation methods for ordinary differential equations
• Two uniform schemes for the singularly perturbed Riccati equation
• Layer-adapted meshes for convection-diffusion problems
• Exponentially fitted one-step methods for the numerical solution of the scalar Riccati equation
• Numerical integration of the differential matrix Riccati equation
• The recursive reduced-order numerical solution of the singularly perturbed matrix differential Riccati equation
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