biharmonic_fd1d, an Octave code which applies the finite difference method to solve the biharmonic equation over an interval, a fourth order two point boundary value problem (BVP) in one spatial dimension.
The boundary value problem has the form:
d^4/dx^4 u(x) = exp(x)
in the interval [-1,+1], with boundary conditions
u (-1) = 0 u (+1) = 0
u'(-1) = 0 u'(+1) = 0
To compute a finite difference approximation, a set of N equally spaced nodes is defined over the interval, and, at each interior node, a discretized version of the BVP is written, with the fourth derivative approximated by finite differences. The derivative boundary conditions at left and right are used to modify equations #2 and #N-1.
The computer code and data files described and made available on this web page are distributed under the MIT license
biharmonic_fd1d is available in a MATLAB version and an Octave version.
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