Numerical Experimentation on the Korteweg-De Vries Equation.
NEW YORK UNIV BRONX DEPT OF ELECTRICAL ENGINEERING AND COMPUTER SCIENCE
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Some numerical experiments are described for solving one-dimensional partial differential equations by explicit finite-difference schemes. The numerical schemes were operated in their unstable regions in order to illustrate the effect of numerical instabilities. As expected, it was found that numerical instabilities occurred when the Courant, Fredrichs, and Lewy criterion was violated. Theoretical instability growth rates were compared with actual growth rates of the computed results and found very close agreement. The initial numerical noise from which the instability grew was found and is the expected single-precision truncation error of the computer used in the calculations.
- Numerical Mathematics