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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).

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).

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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I need a MATLAB solution to the excercise below using the Shooting-method, to get a better understanding about this technique.

Previously I received my answer of my free-question as following (I don't get why we are using cosines here):

d2Tdx2=-25d2Tdx2+25=0

let ddx=Dso solved be the method of differential equation

m2+25=0m=±5iT(x) = A cos (5x) + B sin(5x)at T(x=0) = 40at T(x=10 )=20040 = A + 0 A=40 200 = 40 cos(50) + B sin(50) 200 =40 *0.964  -0.26B=38.598-0.26B161.40=-0.26B-620.7=BT = 40 cos(5x) - 620.7 sin(5x) 

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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