1. Euler's method a. Newton's law of cooling says that the temperature of a body changes at a rate proportional to the difference between its temperature (T) and the ambient temperature (Ta): dT = -k(T – Ta) dt where the temperatures are in the unit of Celsius, t=time (min), k= the proportionality constant (per minute). Suppose at timet = 0 min we place a T = 20°C cup of water in a refrigerator, Ta = 4°C. Use Euler's method to compute the temperature from t = 0 to t = 6 min using a step size of 2 min if k = 0.05 min¬1. Note: only a numerical solution based on the Euler's method will be accepted (no analytical ODE solution is needed iterative equation, initial condition, . %3D Please make sure to include your
1. Euler's method a. Newton's law of cooling says that the temperature of a body changes at a rate proportional to the difference between its temperature (T) and the ambient temperature (Ta): dT = -k(T – Ta) dt where the temperatures are in the unit of Celsius, t=time (min), k= the proportionality constant (per minute). Suppose at timet = 0 min we place a T = 20°C cup of water in a refrigerator, Ta = 4°C. Use Euler's method to compute the temperature from t = 0 to t = 6 min using a step size of 2 min if k = 0.05 min¬1. Note: only a numerical solution based on the Euler's method will be accepted (no analytical ODE solution is needed iterative equation, initial condition, . %3D Please make sure to include your
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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Transcribed Image Text:1. Euler's method
a. Newton's law of cooling says that the temperature of a body changes at a rate proportional
to the difference between its temperature (T) and the ambient temperature (Ta):
dT
= -k(T – Ta)
dt
where the temperatures are in the unit of Celsius, t=time (min), k= the proportionality
constant (per minute).
Suppose at timet = 0 min we place a T = 20°C cup of water in a refrigerator, Ta = 4°C.
Use Euler's method to compute the temperature from t = 0 to t = 6 min using a step
size of 2 min if k = 0.05 min¯1.
Note: only a numerical solution based on the Euler's method will be accepted (no
analytical ODE solution is needed
iterative equation, initial condition, .
Please make sure to include your
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