The stability criteria for solution to the difference equation corresponding to the heat equation using the explicit approach is aAt 1. Assume that & = 0.1. If I choose Ax = 1 mm what will happen to the solution when At is set to 0.001 second?
The stability criteria for solution to the difference equation corresponding to the heat equation using the explicit approach is aAt 1. Assume that & = 0.1. If I choose Ax = 1 mm what will happen to the solution when At is set to 0.001 second?
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter11: Differential Equations
Section11.1: Solutions Of Elementary And Separable Differential Equations
Problem 59E: According to the solution in Exercise 58 of the differential equation for Newtons law of cooling,...
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Transcribed Image Text:QUESTION 3
The stability criteria for solution to the difference equation corresponding to the heat equation using the explicit approach is
aAt
< 1. Assume that a = 0.1. If I choose Ax =1 mm what will happen to the solution when At is set to 0.001 second?
(Ax)²
It will diverge as it will not be stable
Solution will be equal to the analytical solution
It will not be accurate
O It will converge
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