Advanced Numerical Schemes for Singular Perturbation Problems

This volume offers a comprehensive introduction, detailed exposition, and critical evaluation of numerical techniques designed to address singularly perturbed differential equations. Distinguished by the presence of boundary and interior layers-regions where solutions exhibit rapid variation under small perturbation parameters-these problems present unique analytical and computational challenges.Structured across four chapters, the book begins with a foundational discussion of singular perturbation theory, including essential definitions, conceptual motivations, and a critical survey of the literature that traces the historical development of the field. This opening framework establishes the context for subsequent chapters, which explore a range of numerical schemes and their practical application to diverse singular perturbation problems. By combining theoretical insights with methodological rigor, the text provides readers with both a solid grounding in the subject and a clear pathway to advanced computational approaches.