A function is given by f(x) = 2x - e-6. Now answer the following: (a) Approximate the derivative of f(x) at xo = 0.5 with step size h = 0.2 using the forward difference method up to 5 significant figures. Approximate the derivative of f(x) at xo = 0.5 with step size h = 0.2 using the central difference method up to 6 significant figures. (c) (4+4 marks) Calculate the truncation error of f(x) at xo = 2 using h= 1, 0.1, 0.01, 0.0001 in both of the above mentioned methods.
A function is given by f(x) = 2x - e-6. Now answer the following: (a) Approximate the derivative of f(x) at xo = 0.5 with step size h = 0.2 using the forward difference method up to 5 significant figures. Approximate the derivative of f(x) at xo = 0.5 with step size h = 0.2 using the central difference method up to 6 significant figures. (c) (4+4 marks) Calculate the truncation error of f(x) at xo = 2 using h= 1, 0.1, 0.01, 0.0001 in both of the above mentioned methods.
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. A function is given by f(x) = 2x - e-6. Now answer the following:
Approximate the derivative of f(x) at xo = 0.5 with step size h = 0.2 using the forward difference
method up to 5 significant figures.
Approximate the derivative of f(x) at xo = 0.5 with step size h = 0.2 using the central difference
method up to 6 significant figures.
=
(c) (4+4 marks) Calculate the truncation error of f(x) at xo = 2 using h
above mentioned methods.
1, 0.1, 0.01, 0.0001 in both of the
Compute Dat ro = 0.2 using Richardson extrapolation method up to 6 significant figures and
calculate the truncation error.
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