Extrapolated ADI Crank–Nicolson Orthogonal Spline Collocation for Coupled Burgers' Equations

We use extrapolated alternating direction implicit Crank-Nicolson orthogonal spline collocation with splines of order r to solve the coupled Burgers' equations in two space variables and two unknown functions. The scheme is initialized with an alternating direction implicit predictor-corrector method. We show theoretically that the norm of the error at each time level is of order r in space and of order 2 in time. Our numerical results confirm these theoretical orders.