A single sweep AGE algorithm based on off-step discretization for the solution of viscous Burgers' equation on a variable mesh (Q2018664)

The main aim of the paper is to propose an efficient numerical algorithm for solving two-point boundary value problems for second-order nonlinear differential equations. In previous works of one of the authors, a third-order off-step discretization scheme on a variable mesh and the couple alternating group explicit (CAGE) method were proposed for solving singular nonlinear boundary value problems. In this paper, the authors develop a new single sweep alternating group explicit (AGE) iteration method, which is similar to the CAGE method, and apply it together with the off-step discretization on a variable mesh for solving the Burgers' equation. The algorithm is shown to be convergent and more efficient than the double sweep AGE method. Furthermore, it efficiently solves singular problems as well. Numerical experiments are given to illustrate the convergence and the efficiency of the algorithm.