Computationally Efficient Technique for Solving ODE Systems Exhibiting Initial and Boundary Layers

Abstract EN

A computational technique based on asymptotic analysis for solving singularly perturbed ODE systems involving a small parameter ϵ is considered.

The focus is on second-order systems, but the procedure is also applicable for first-order systems.

Both initial value and boundary value problems will be solved.

The application of the method is considered over the entire time domain for a wide range of ϵ and the resulting approximation is compared with the direct numerical solution.

The convection-diffusion problem from fluid mechanics and the telegraph equation from electrical engineering are considered.