About this Research Topic
In computational mathematics, the challenge of solving singularly perturbed differential problems is significant. These problems, characterized by equations in which the highest derivative is multiplied by a very small parameter ε, manifest thin boundary or interior layers as ε approaches zero. Traditional analytical methods struggle with the rapid changes within these layers, making numerical solutions essential. As these issues intensify with smaller values of ε, the development of ε-uniform convergent numerical methods has become critical.
This Research Topic aims to establish and refine robust numerical schemes that enhance accuracy, stability, and rate of convergence across varying parameters. The goal is not only to address existing computational challenges but also to extend the capabilities of numerical methods in handling complex, layered solutions typical of singularly perturbed problems.
To further progress in this field, contributions that push the boundaries of current methodologies are essential. To that end, we are seeking submissions that cover a broad spectrum of related areas, including but not limited to:
- Novel algorithms for both ordinary and partial differential equations
- Theoretical advancements and heuristic approaches in numerical computations
- Systematic reviews of existing methods and their efficiencies
- Practical applications and case studies demonstrating the effectiveness of proposed solutions
Each manuscript should be a complete, self-contained original contribution, accessible to a wide audience within the computational mathematics community and aligned with the latest research trends and demands.
This Research Topic aims to establish and refine robust numerical schemes that enhance accuracy, stability, and rate of convergence across varying parameters. The goal is not only to address existing computational challenges but also to extend the capabilities of numerical methods in handling complex, layered solutions typical of singularly perturbed problems.
To further progress in this field, contributions that push the boundaries of current methodologies are essential. To that end, we are seeking submissions that cover a broad spectrum of related areas, including but not limited to:
- Novel algorithms for both ordinary and partial differential equations
- Theoretical advancements and heuristic approaches in numerical computations
- Systematic reviews of existing methods and their efficiencies
- Practical applications and case studies demonstrating the effectiveness of proposed solutions
Each manuscript should be a complete, self-contained original contribution, accessible to a wide audience within the computational mathematics community and aligned with the latest research trends and demands.
Keywords: singularly perturbed problems, efficient numerical schemes, robust numerical methods, time delay, spatial delay, differential-difference equations
Important Note: All contributions to this Research Topic must be within the scope of the section and journal to which they are submitted, as defined in their mission statements. Frontiers reserves the right to guide an out-of-scope manuscript to a more suitable section or journal at any stage of peer review.
