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Maximum norm convergence analysis of extrapolated Crank-Nicolson orthogonal spline collocation for Burgers’ equation in one space variable. (English) Zbl 1405.65131

Summary: Burgers’ 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 \(r\geq 3\) 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.

MSC:

65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
35Q53 KdV equations (Korteweg-de Vries equations)
65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
65D07 Numerical computation using splines
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs

Software:

COLROW; ARCELO
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Full Text: DOI

References:

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