A Review Of Solving and Applications Singularly Perturbed Problems - Ahmed R Khlefha (International Journal of Science and Mathematics Education, 2024)
In this paper, Spline techniques have become prominent lately due to their effectiveness in addressing singular perturbation boundary value problems. These issues, defined by a boundary layer or a minor parameter associated with a derivative term, pose difficulties due to swift fluctuations in solutions adjacent to the boundary. Solutions to singularly perturbed involving both positive and negative changes in a spatial variable are shown in this review article. The methods presented here are algorithmic in nature. The singular perturbation that arises in neural activity simulation and the approaches proposed by numerous investigators between 2004 and 2024 are the only ones covered in this review. A variety of types of singularly perturbed were reviewed, including ordinary delay differential . Discovering what numerical and analytical strategies have been created in the past decade to address these types of issues is the primary objective of this review. Its secondary objective is to encourage academics to come up with novel, strong approaches to resolving related issues.