Application of method of collocation on lines for solving nonlinear hyperbolic problems
Author:
E. N. Houstis
Journal:
Math. Comp. 31 (1977), 443456
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 CrankNicholson discretization in time is studied and convergence rates of the collocationCrankNicholson procedure are established. Finally, the superconvergence is verified at particular points for linear hyperbolic problems.
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718197704433792
PII:
S 00255718(1977)04433792
Keywords:
Collocation on lines method,
nonlinear hyperbolic problems
Article copyright:
© Copyright 1977
American Mathematical Society
