ANALYSIS OF NUMERICAL SCHEMES TO SINGULAR PERTURBATION PROBLEMS

The primary goal of this book is to present evaluate and analyze efficient numerical methods for solving a specific class of singularly perturbed differential equations characterized by boundary and interior layer behaviors. Organized into six chapters the book begins with a detailed overview of definitions motivations singular perturbation problems differential-difference equations boundary layers and a comprehensive literature review. Subsequent chapters introduce advanced numerical methods such as adaptive splines numerical integration on specialized meshes trigonometric splines and fitted numerical schemes using the backward Euler method to address interior layer problems differential-difference equations and singularly perturbed parabolic differential-difference equations. These studies underscore the significance of developing numerical techniques for singularly perturbed differential-difference equations. The research emphasizes creating simple non-asymptotic user-friendly and efficient methods that are easily adaptable for computer implementation with minimal preparation.