Collocation method using artificial viscosity for solving stiff singularly perturbed turning point problem having twin boundary layers

A numerical scheme is proposed to solve singularly perturbed two-point boundary value problems with a turning point exhibiting twin boundary layers. The scheme comprises a B-spline collocation method on a uniform mesh, which leads to a tridiagonal linear system. Asymptotic bounds are established for the derivative of the analytical solution of a turning point problem. The analysis is done on a uniform mesh, which permits its extension to the case of adaptive meshes which may be used to improve the solution. The design of an artificial viscosity parameter is confirmed to be a crucial ingredient for simulating the solution of the problem. Some relevant numerical examples are also illustrated to verify computationally the theoretical aspects.