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Asked Oct 31, 2019

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#16 from this handout

From Numerical Analysis 8th Edition by Richard Burden, Section 3.4

Step 1

Consider the function ** f(x) = e^{x} **and

* *

Let the polynomial passing through the above points:

Step 2

Then

*a _{0} = f(x_{0}) = f (0) = e^{0 }= 1*

* *

*a _{1} = f(x_{1}) = f (0.25) = e^{.25 }= 1.2840*

*a _{2} = f(x_{2}) = f (0.75) = e^{0.75 }= 2.1170*

* *

*a _{3} = f(x_{3}) = f (1) = e ^{1 }= 2.7182*

we have *n = 3 *

*h _{0} = x_{1} – x_{0 }= 0.25*

_{ }

*h _{1} = x_{2} – x_{1 }= 0.50*

* *

*h _{2} = x_{3} – x_{2} = 0.25*

Step 3

Using the above conditions and ...

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