A Quadratic B-Spline Collocation Method for a Singularly Perturbed Semilinear Reaction-Diffusion Problem with Discontinuous Source Term

In this paper, a quadratic B-spline collocation method is developed to solve a singularly perturbed semilinear reaction-diffusion problem with a discontinuous source term. The discontinuous source term leads to a jump in the second-order derivative of the exact solution at the discontinuous point. A quadratic B-spline collocation method on a Shishkin-type mesh is used to discretized the singularly perturbed problem on the left and right sides of the discontinuous point, respectively. The collocation equations at the discontinuous point are obtained using the conditions satisfied at the discontinuous point. It is shown that the scheme is stable and almost second-order uniformly convergent. Numerical experiments support the theoretical results.