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

DOI:
https://doi.org/10.1090/S0025-5718-1977-0443379-2

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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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1977-0443379-2

Keywords:
Collocation on lines method,
nonlinear hyperbolic problems

Article copyright:
© Copyright 1977
American Mathematical Society