A rational spectral collocation method for third-order singularly perturbed problems

A new numerical method is developed for solving a class of third-order singularly perturbed boundary value problems. First of all, the given problem is transformed into a system of two ordinary differential equations (ODEs) subject to suitable initial and boundary conditions. Then, the rational spectral collocation method in barycentric form with sinhsinh transformation is applied to solve the system of ODEs. According to the asymptotic analysis, the location and width of boundary layer of the given problem, which are chosen as parameters in the sinhsinh transformation, can be determined. Ample numerical experiments are presented to illustrate the computational efficiency and accuracy of the our method.