SWAGE algorithm for the cubic spline solution of nonlinear viscous Burgers’ equation on a geometric mesh

In this paper, we discuss the single sweep alternating group explicit (SWAGE) and Newton-SWAGE iteration methods to solve the non-linear ordinary differential equation y″ = f(x, y, y′) subject to given natural boundary conditions, along with a third order cubic spline numerical method on a geometric mesh. It is applicable to both singular and non-singular problems. The convergence of the SWAGE iteration method is discussed in detail. We compared the results of proposed SWAGE iteration method with the results of corresponding two parameter alternating group explicit (TAGE) iteration methods to demonstrate computationally the efficiency of the proposed method.