A single sweep AGE algorithm on a variable mesh based on off-step discretization for the solution of nonlinear Burgers' equation (Q470646)

Summary: We discuss a new single sweep alternating group explicit (AGE) iteration method, along with a third-order numerical method based on off-step discretization on a variable mesh to solve the nonlinear ordinary differential equation \(y''=f(x,y,y')\) subject to given natural boundary conditions. Using the proposed method, we have solved Burgers' equation both in singular and nonsingular cases, which is the main attraction of our work. The convergence of the proposed method is discussed in detail. We compared the results of the proposed iteration method with the results of the corresponding double sweep alternating group explicit iteration methods to demonstrate computationally the efficiency of the proposed method.