Solving second-order singularly perturbed ODE by the collocation method based on energetic Robin boundary functions

Abstract

for a second-order singularly perturbed ordinary differential equation (ODE) under the Robin type boundary conditions, we develop an energetic Robin boundary functions method (ERBFM) to find the solution, which automatically satisfies the Robin boundary conditions. For the non-singular ODE the Robin boundary functions consist of polynomials, while the normalized exponential trial functions are used for the singularly perturbed ODE. The ERBFM is also designed to preserve the energy, which can quickly find accurate numerical solutions for the highly singularly perturbed problems by a simple collocation technique.