Summary
The ALGOL-procedure1 char2 presented in this paper can be applied to the initial or initial-boundary value problem of a quasilinear hyperbolic differential equation of second order. A method of characteristics is combined with extrapolation to the limit. Thus, the results are very accurate. The same accuracy can also be obtained if the initial values are only piecewise smooth.
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References
Bulirsch, R., Stoer, J.: Asymptotic upper and lower bounds for results of extrapolation methods. Numer. Math.8, 93–104 (1966)
Hackbusch, W.: On a method of characteristics for solving a hyperbolic equation of second order. Computing20, 47–60 (1978)
Stoker, J.J.: Water waves. New York: Interscience 1957
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Editor's Note: In this fascile, prepublication of algorithms from the Approximation series of the Handbook for Automatic Computation is continued. Algorithms are published in ALGOL 60 reference language as approved by the IFIP. Contributions in this series should be styled after the most recently published ones
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Dittrich, S., Hackbusch, W. A method of characteristics solving the initial-boundary value problem of a hyperbolic differential equation of second order. Numer. Math. 34, 217–234 (1980). https://doi.org/10.1007/BF01396700
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DOI: https://doi.org/10.1007/BF01396700