Rational Spectral Collocation Combined with Singularity Separation Method for Second-Order Singular Perturbation Problems

Novel rational spectral collocation is presented in combination with singularity separation method for the second-order singularly perturbed boundary-value problems. The solution is presented in the form u = w + υ; where w is the solution of the corresponding third boundary-value problem and υ is a singular function with explicit expression. The auxiliary third boundary-value problem is solved by the rational spectral collocation method combined with the asymptotic theory (RSCAT). According to the asymptotic analysis, the parameters of the sinh-transformation can be determined according to the location and width of the boundary layers. The parameters in the singular correction can be determined by the boundary conditions of the original problem. The numerical experiments were carried out to demonstrate the computational efficiency and accuracy of the proposed method. © 2023, Springer Nature Switzerland AG.