Parameter-uniformly convergent exponential spline difference scheme for singularly perturbed semilinear reaction–diffusion problems Original Research Article

We consider a Dirichlet boundary value problem for singularly perturbed semilinear reaction–diffusion equation. The problem is discretized using an exponential spline difference scheme derived on the basis of splines in tension on piecewise-uniform Shishkin type mesh. The convergence analysis is given and the method is shown to be almost second order accurate in the discrete maximum norm, uniformly in the perturbation parameter εε. Numerical experiments are conducted to demonstrate the theoretical results.