Taylor series in Numerical method.

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Truncation Error and The Taylors Series.

• Prepared by B.Anil Kumar

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Truncation Error

• Truncation error is an error caused by
  terminating or truncating an infinite process by
  an finite one.

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The Taylors series.
Taylors series predicts a function value at one
point in terms of the function value and its
derivatives at another point.
The Taylors series expansion of a function is
.(1)
Here
is the remainder which includes all the terms
from (n1) th
Term to infinity and
is the step size.
For Taylors series (1), approximations with
different order are as follow-
Zeroth order approximation-
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The Taylors series.(continue)
1st order approximation -
2nd order approximation -
3rd order approximation-
Similarly if we proceed, thenth order
approximation -
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Example-
at xi11 for xi0.2.
Use Taylors series to estimate
Employ the zero, 1st, 2nd order approximations
and compute the et for each case.
Ans-
Given that
and xi11, xi0.2. So h0.8.
Now
The Taylors series is
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Continue
Zeroth order-
f(1) f(0.2)e-0.20.8187308
1st order-
f(1)0.162323
f(1)0.424317
2nd order-
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Example-
at xi11 for xi0.2.
Use Taylors series to estimate
Employ the zero, 1st, 2nd order approximations
and compute the ea for each case.
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Thank You ALL

• Presented by
• Boina Anil Kumar
• Asst.Prof in Mathematics
• MITS, Rayagada.
• Odisha, India
• E-mail anil.anisrav_at_gmail.com
• Visit at http//www.mits.edu.in/academics.phpfac
  ulty_BSH-tab