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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

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A method of fractional steps for scalar conservation laws without the CFL condition
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by Helge Holden and Nils Henrik Risebro PDF
Math. Comp. 60 (1993), 221-232 Request permission

Abstract:

We present a numerical method for the n-dimensional initial value problem for the scalar conservation law $u{({x_1}, \ldots ,{x_n},t)_t} + \sum _{i = 1}^n{f_i}{(u)_{{x_1}}} = 0, u({x_1}, \ldots ,{x_n},0) = {u_0}({x_1}, \ldots ,{x_n})$. Our method is based on the use of dimensional splitting and Dafermos’s method to solve the one-dimensional equations. This method is unconditionally stable in the sense that the time step is not limited by the space discretization. Furthermore, we show that this method produces a subsequence which converges to the weak entropy solution as both the time and space discretization go to zero. Finally, two numerical examples are discussed.
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Additional Information
  • © Copyright 1993 American Mathematical Society
  • Journal: Math. Comp. 60 (1993), 221-232
  • MSC: Primary 65M12; Secondary 35L65
  • DOI: https://doi.org/10.1090/S0025-5718-1993-1153165-5
  • MathSciNet review: 1153165