The one-dimensional heat equation ut + a ux = :0 is discretised using the forward Euler time scheme and a two node centred spatial scheme. This discretisation results in the following equation ● n+1 ui – u? At a n+1 Ui+1 - n+1 ui-1 24x Check the consistency of the discrete equation and state the order of the truncation error for At and Ax. Using the modified equation method, investigate the stability of the discrete equation. Comment on any stability limitations in terms of choice of At Comment on the implications of this scheme with regards to numerical diffusion and dispersion, if any.

The one-dimensional heat equation ut + a ux = :0 is discretised using the forward Euler time scheme and a two node centred spatial scheme. This discretisation results in the following equation ● n+1 ui – u? At a n+1 Ui+1 - n+1 ui-1 24x Check the consistency of the discrete equation and state the order of the truncation error for At and Ax. Using the modified equation method, investigate the stability of the discrete equation. Comment on any stability limitations in terms of choice of At Comment on the implications of this scheme with regards to numerical diffusion and dispersion, if any.

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Question

The one-dimensional heat equation
ut + a ux = 0
is discretised using the forward Euler time scheme and a two node centred spatial scheme. This
discretisation results in the following equation
n+1
Ui u?
-
At
= a
n+1
Ui+1
n+1
ui-1
24x
● Check the consistency of the discrete equation and state the order of the truncation error for
At and Ax.
Using the modified equation method, investigate the stability of the discrete equation.
Comment on any stability limitations in terms of choice of At.
Comment on the implications of this scheme with regards to numerical diffusion and
dispersion, if any.

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