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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Concept explainers

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

Question

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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