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ME17, Summer, 2008
SUMMARY SHEET
1.
Numerical vs. Analytical solutions
.
Analytical solutions are given by mathematical formulae.
Numerical solutions are a set of numbers produced by a computer.
2. Algorithms
are the procedures by which numerical solutions are obtained. They come in two broad
classes:
Direct
algorithms give the numerical answer after a finite and specific number of steps.
Iterative
algorithms involve sequential estimations (iterations) toward the answer.
Taylor series
are an important
tool in deriving and analyzing algorithms.
You should know how to compute the Taylor series of a
function.
3.
Numerical methods are subject to errors
. There are two primary sources of error.
Truncation error
refers to the errors inherent in the algorithm, which is always an approximation to the true solution.
Roundoff error
refers to the error associated with the finite word length of floating point numbers in a
computer.
4.
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 Summer '07
 Milstein

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