Linearization techniques for singularly-perturbed initial-value problems of ordinary differential equations

DOI10.1016/j.amc.2004.06.002zbMath1067.65065OpenAlexW2114071527MaRDI QIDQ1774829

Juan I. Ramos

Publication date: 4 May 2005

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

Full work available at URL: https://doi.org/10.1016/j.amc.2004.06.002

zbMATH Keywords

numerical examplesTaylor series expansionSingular perturbationsInitial-value problemsAdaptive mesh refinementLinearization methodsRiccati's equations

Mathematics Subject Classification ID

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

Related Items (6)

A PIECEWISE APPROXIMATE ANALYTICAL SOLUTION FOR NONLINEAR TRANSIENT CIRCUITS USING ADAPTIVE STEP SIZE L-STABLE INTEGRATION SCHEME ⋮ Piecewise-quasilinearization techniques for singularly perturbed Volterra integro-differential equations ⋮ A non-standard explicit integration scheme for initial-value problems ⋮ Unnamed Item ⋮ A recent survey on computational techniques for solving singularly perturbed boundary value problems ⋮ A new algorithm appropriate for solving singular and singularly perturbed autonomous initial-value problems

Cites Work

• Linearization methods in classical and quantum mechanics
• Piecewise quasilinearization techniques for singular boundary-value problems
• A uniform scheme for the singularly perturbed Riccati equation
• Uniform and optimal schemes for stiff initial-value problems
• New initial-value method for singularly perturbed boundary-value problems
• A boundary value technique for singular perturbation problems
• A piecewise time-linearized method for the logistic differential equation
• An asymptotic initial value method for boundary value problems for a system of singularly perturbed second order ordinary differential equations.
• Numerical patching method for singularly perturbed two-point boundary value problems using cubic splines.
• A computational procedure for solving a chemical flow reactor problem using shooting method
• A computational method for solving singular perturbation problems using exponentially fitted finite difference schemes
• Linearized methods for ordinary differential equations
• Exponentially fitted one-step methods for the numerical solution of the scalar Riccati equation
• Initial-value methods for second-order singularly perturbed boundary- value problems
• Optimal uniform finite difference schemes of order two for stiff initial value problems
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