**diff2_center**,
a MATLAB code which
interactively uses centered differences to estimate the second derivative
of a function f(x), using a stepsize h.

If a call is made of the form

yp = diff2_center ( f_string, x, h );then x can be a vector. Otherwise, x should be a single value.

The program returns yp, the centered difference estimate for f"(x).

The program can be invoked by a function call, in which case the string specifying f(x) must be quoted:

yp = diff2_center ( 'x^2', 1.0, 0.01 )or, if called with no arguments, it will request them:

yp = diff2_center ( ); Enter function formula, like x^2: x^2 Enter evaluation point, x: 1.0 Enter stepsize, h: 0.01

The function is specified as a string which is either:

- a MATLAB expression using the argument 'x';
- the name of an M-file followed by the argument '(x)'.

The string should not contain any spaces between symbols, except when it is passed as a function argument in quotes.

It is not necessary to use the "dot" notation for expressions involving '*', '/', or '^', but it doesn't hurt either.

Examples of function specifications:

x^2 x.^2 3/(x^4+5*x-6) sin(7*x)*sqrt(x)/8 wiggle(x) <-- where "wiggle.m" is a user-provided M file.

The computer code and data files made available on this web page are distributed under the GNU LGPL license.

**diff2_center** is available in
a MATLAB version.

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- diff2_center.m the source code.