One of the most prominent and complicated tasks in the field of numerical analysis is the precise approximation of the interaction between convective and diffusive processes. This is attributed in part to their strong relationship with boundary layer theory and singular perturbation problems. There is a wide variety and frequent occurrence of singularly perturbed problems in science and engineering. In most cases, the solutions to singularly perturbed problems show multiscale phenomena as well as steep boundary and interior layers, which can be observed in flow experiments. Sometimes it is difficult to derive asymptotic solutions of singularly perturbed problems and it can be challenging to demonstrate with absolute conviction that the asymptotic approximations derived are accurately representations of the exact solutions. Thus, the numerical treatment of such processes is essential yet challenging, particularly for small singular perturbation parameters or large Reynolds numbers.
The main goal of this Research Topic is to provide a platform for researchers to present the latest advances in singularly perturbed problems and their asymptotic analysis, including analytical and numerical methods for singularly perturbed problems, and real-world applications of singularly perturbed problems.
This Research Topic welcomes high-quality original research papers on all aspects of the theory and numerics of singularly perturbed problems. Both theoretical and numerical analysis of singularly perturbed problems and their applications fall within the scope of this collection. Topics of interest include, but are not limited to:
- Singularly perturbed ordinary and partial differential equations (initial or boundary value problems)
- Singularly perturbed problems with a delay or advance
- Singularly perturbed integro-differential equations
- Singularly perturbed problems with discontinuous data
- Singularly perturbed turning point problems
- Singularly perturbed differential-difference problems
- Singularly perturbed control problems
- Mesh generation for singularly perturbed problems
One of the most prominent and complicated tasks in the field of numerical analysis is the precise approximation of the interaction between convective and diffusive processes. This is attributed in part to their strong relationship with boundary layer theory and singular perturbation problems. There is a wide variety and frequent occurrence of singularly perturbed problems in science and engineering. In most cases, the solutions to singularly perturbed problems show multiscale phenomena as well as steep boundary and interior layers, which can be observed in flow experiments. Sometimes it is difficult to derive asymptotic solutions of singularly perturbed problems and it can be challenging to demonstrate with absolute conviction that the asymptotic approximations derived are accurately representations of the exact solutions. Thus, the numerical treatment of such processes is essential yet challenging, particularly for small singular perturbation parameters or large Reynolds numbers.
The main goal of this Research Topic is to provide a platform for researchers to present the latest advances in singularly perturbed problems and their asymptotic analysis, including analytical and numerical methods for singularly perturbed problems, and real-world applications of singularly perturbed problems.
This Research Topic welcomes high-quality original research papers on all aspects of the theory and numerics of singularly perturbed problems. Both theoretical and numerical analysis of singularly perturbed problems and their applications fall within the scope of this collection. Topics of interest include, but are not limited to:
- Singularly perturbed ordinary and partial differential equations (initial or boundary value problems)
- Singularly perturbed problems with a delay or advance
- Singularly perturbed integro-differential equations
- Singularly perturbed problems with discontinuous data
- Singularly perturbed turning point problems
- Singularly perturbed differential-difference problems
- Singularly perturbed control problems
- Mesh generation for singularly perturbed problems