Problem 3. An insulated heated rod with a uniform heat source can be modeled with the Poisson equation: d²T dx² = -f(x) Given a heat source f(x) 25°C/m² and the boundary conditions T(x = 0) = 40°C and T(x = 10) = 200°C, solve for the temperature

Calculus: Early Transcendentals
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Author:James Stewart
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Chapter1: Functions And Models
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I need a complete solution to the excercise below using Shooting-method.

I did some researches but still can't understand the differences between Shooting-method and the likes of Euler's method, Runge Kutta 2nd/4th order.

Problem 3. An insulated heated rod with a uniform heat source can be modeled
with the Poisson equation:
d²T
dx²
= -f(x)
=
=
Given a heat source f(x) 25°C/m² and the boundary conditions
T(x = 0) = 40°C and T(x = 10) = 200°C, solve for the temperature
distribution with (a) the shooting method and (b) the finite-difference
method (Ax = 2).
Transcribed Image Text:Problem 3. An insulated heated rod with a uniform heat source can be modeled with the Poisson equation: d²T dx² = -f(x) = = Given a heat source f(x) 25°C/m² and the boundary conditions T(x = 0) = 40°C and T(x = 10) = 200°C, solve for the temperature distribution with (a) the shooting method and (b) the finite-difference method (Ax = 2).
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