A parameter-uniform numerical method for singularly perturbed Burgers’ equation

In this article, we propose a parameter-uniformly convergent numerical method for singularly perturbed Burgers’ initial-boundary value problem. First, the Burgers’ partial differential equation is semi-discretized in time using Crank–Nicolson finite difference method to yield a set of singularly perturbed nonlinear ordinary differential equations in space. The resulting two-point boundary value nonlinear singularly perturbed problems are linearized using Newton quasilinearization technique, and then, we apply fitted operator finite difference method to exhibit the layer nature of the solution. It is shown that the method converges uniformly with respect to the perturbation parameter. Numerical experiments are carried out to confirm the parameter-uniform nature of the scheme which is second-order convergent in time and first-order convergent in space.