3. For the equation: t(3+ +100 = e-t a- Using a spreadsheet, plot the function f(t) from t = 0 to t = 1 and At = 0.05 b- Using the initial guesses of t= 0 and t = 1, conduct 4 iterations using the Regula Falsi method to determine the root of the function. Calculate the relative approximation error of the last iteration. c- Using the initial guesses of t= 0 andt = 1, conduct 4 iterations using the secant method to determine the root of the function. Calculate the relative approximation error of the last iteration. d- Using the initial guess t= 0.1, conduct 4 iterations using the Newton-Raphson method to determine the root of the function. Calculate the relative approximation error of the last iteration. e- Using the initial guess t 0, conduct 4 iterations using the single-point method to determine the root of the function. Calculate the relative approximation error of the last iteration. f- Compare the convergence rate of the last 3 iterations of all the techniques in b) to e).
3. For the equation: t(3+ +100 = e-t a- Using a spreadsheet, plot the function f(t) from t = 0 to t = 1 and At = 0.05 b- Using the initial guesses of t= 0 and t = 1, conduct 4 iterations using the Regula Falsi method to determine the root of the function. Calculate the relative approximation error of the last iteration. c- Using the initial guesses of t= 0 andt = 1, conduct 4 iterations using the secant method to determine the root of the function. Calculate the relative approximation error of the last iteration. d- Using the initial guess t= 0.1, conduct 4 iterations using the Newton-Raphson method to determine the root of the function. Calculate the relative approximation error of the last iteration. e- Using the initial guess t 0, conduct 4 iterations using the single-point method to determine the root of the function. Calculate the relative approximation error of the last iteration. f- Compare the convergence rate of the last 3 iterations of all the techniques in b) to e).
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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Please do all parts.
Transcribed Image Text:3. For the equation:
t(3+100 = e-t
a- Using a spreadsheet, plot the function f(t) from t = 0 to t =1 and At = 0.05
b- Using the initial guesses of t= 0 and t= 1, conduct 4 iterations using the Regula Falsi
method to determine the root of the function. Calculate the relative approximation
error of the last iteration.
c- Using the initial guesses of t= 0 and t = 1, conduct 4 iterations using the secant
method to determine the root of the function. Calculate the relative approximation
error of the last iteration.
d- Using the initial guess t= 0.1, conduct 4 iterations using the Newton-Raphson method
to determine the root of the function. Calculate the relative approximation error of the
last iteration.
e- Using the initial guess t= 0, conduct 4 iterations using the single-point method to
determine the root of the function. Calculate the relative approximation error of the
last iteration.
f- Compare the convergence rate of the last 3 iterations of all the techniques in b) to e).
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