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Numerical stability of Crank-Nicolson for linear advection equation. Determine under which conditions the Crank-Nicolson scheme for the linear advection equa- cion vn+1 a v+1 – v}_1 - n+1° 'j-1 =0 2Ar j+1 At 2Ar s numerically stable.

Numerical stability of Crank-Nicolson for linear advection equation. Determine under which conditions the Crank-Nicolson scheme for the linear advection equa- cion vn+1 a v+1 – v}_1 - n+1° 'j-1 =0 2Ar j+1 At 2Ar s numerically stable.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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use Von Neumann analysis to derive the numerical stability.

Numerical stability of Crank-Nicolson for linear advection equation. Determine under which conditions the Crank-Nicolson scheme for the linear advection equa- tion v+1 – v vn+1 j+1 2Ax vn+1 Pj-1 v+1 - v a = 0 At 2Ax is numerically stable.
Transcribed Image Text:Numerical stability of Crank-Nicolson for linear advection equation. Determine under which conditions the Crank-Nicolson scheme for the linear advection equa- tion v+1 – v vn+1 j+1 2Ax vn+1 Pj-1 v+1 - v a = 0 At 2Ax is numerically stable.
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