Numerical methods for singularly perturbed differential equations

Autori

• Hans-Görg Roos

Parametri

• Matematica
• Springer series in computational mathematics

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The analysis of singular perturbed differential equations began early in the century with approximate solutions derived from asymptotic expansions, a technique that gained traction in the mid-1960s. While several textbooks cover its principal ideas and methods, there are instances where asymptotic expansions may be infeasible or fail to simplify the problem, making numerical approximations the only viable alternative. The systematic study of numerical methods for these singular perturbation problems emerged in the 1970s. Despite ongoing advancements, the exposition of new developments in numerical methods has been overlooked, with the notable exception of a textbook that compiles results for ordinary differential equations. Many relevant methods for partial differential equations have emerged since 1980, leaving contemporary researchers to sift through literature to find earlier work. This introductory book aims to provide a structured overview of recent ideas in the numerical analysis of singularly perturbed differential equations while highlighting the numerous open problems in the field, thereby encouraging further exploration. The topics selected reflect the authors' personal interests and expertise.

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Lingua: Inglese

Pubblicato: 1996