1) For the Model Linear Transport Equation (1-D Wave Equation) ди ди + a at ax FTCS method obtained by using first-order forward-difference in time and second-order center-difference in space, a) Derive the stability condition using the von Neumann method, b) Derive the term artificial viscosity.

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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For the Model Linear Transport Equation (1-D Wave Equation)

FTCS method obtained by using first-order forward-difference in time and second-order center-difference in space,

  1. a) Derive the stability condition using the von Neumann method,
  2. b) Derive the term artificial viscosity.

The whole problem is in the attached picture. thank you so much.

1) For the Model Linear Transport Equation (1-D Wave Equation)
ди
ди
+ a
at
ax
FTCS method obtained by using first-order forward-difference in time and second-order
center-difference in space,
a) Derive the stability condition using the von Neumann method,
b) Derive the term artificial viscosity.
Transcribed Image Text:1) For the Model Linear Transport Equation (1-D Wave Equation) ди ди + a at ax FTCS method obtained by using first-order forward-difference in time and second-order center-difference in space, a) Derive the stability condition using the von Neumann method, b) Derive the term artificial viscosity.
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