Studies in numerical nonlinear instability. II. A new look at \(u_ t+uu_ x=0\). (English) Zbl 0612.65053

Vadillo, F.; Sanz-Serna, J. M.

J. Comput. Phys. 66, 225-238 (1986).

[For part I by the second author see SIAM J. Sci. Stat. Comput. 6, 923- 938 (1985; reviewed above).]
It is shown for a leap-frog discretization of equation \(u_ t+uu_ x\) that any particular unstable solution behaves as an attractor of other solutions. The overflow time is estimated and related to the notions of stability threshold and restricted stability.

Reviewer: V.A.Kostova

MSC:

65M12	Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
35L60	First-order nonlinear hyperbolic equations

Keywords:

nonlinear instability; leapfrog schemes; Crank-Nicolson; attractor; overflow

Citations:

Zbl 0612.65052

References:

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