Numerical solution of general singular perturbation boundary value problems based on adaptive cubic splineR. Mohammadi (pp. 11-21)
Abstract.We use adaptive cubic spline functions to develop a numerical method for solving a class of singular perturbation two-point boundary value problems. The scheme derived in this method is second order accurate. Convergence of the method is shown. The resulting linear system of equations has been solved by using a tri-diagonal solver. Numerical examples are given to show the applicability and eficiency of our method.
Keywords:second-order boundary value problem, adaptive cubic spline, convergence analysis, singular perturbation problems