Maximum norm convergence analysis of extrapolated Crank-Nicolson orthogonal spline collocation for Burgers' equation in one space variable

Abstract

ABSTRACTBurgers' equation in one space variable is a classical example of a non-linear parabolic problem. We discretize this equation in space using orthogonal spline collocation with splines of degree and we use extrapolated Crank-Nicolson scheme for time discretization. The scheme is initialized with a predictor-corrector method. We show theoretically that the maximum norm of the error at each time level is of order r+1 in space and of order 2 in time. Our numerical results confirm these theoretical orders.