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Application of method of collocation on lines for solving nonlinear hyperbolic problems

Author: E. N. Houstis
Journal: Math. Comp. 31 (1977), 443-456
MSC: Primary 65N35
MathSciNet review: 0443379
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Abstract: A collocation on lines procedure based on piecewise polynomials is applied to initial/boundary value problems for nonlinear hyperbolic partial differential equations. Optimal order a priori estimates are obtained for the error of approximation. The Crank-Nicholson discretization in time is studied and convergence rates of the collocation-Crank-Nicholson procedure are established. Finally, the superconvergence is verified at particular points for linear hyperbolic problems.

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Keywords: Collocation on lines method, nonlinear hyperbolic problems
Article copyright: © Copyright 1977 American Mathematical Society