Comparison of some fourth order difference schemes for hyperbolic problems

John Gary

Mathematics and Computers in Simulation (MATCOM), 1975, vol. 17, issue 3, 192-194

Abstract: Our purpose is the comparison of a few difference schemes for application to hyperbolic equations such as those found in computational fluid dynamics. In order to provide a valid comparison we will use the optimal time-step Δt and mesh spacing Δx to achieve a preassigned accuracy. This means we assign an error in the solution to the equation, usually 5% or 0.5% relative error, and then determine the values of Δt and Δx to yield this error with minimal computational effort. In practice one cannot be this precise; however, this is the only reasonable way to compare the schemes. We will describe a graphical means to determine these optimal values for test problems for which the exact solution is known. We will also introduce two predictor-corrector schemes which, to our knowledge, have not previously been applied to hyperbolic equations.

Date: 1975
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:17:y:1975:i:3:p:192-194

DOI: 10.1016/S0378-4754(75)80052-8

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