biharmonic_fd1d


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.

Licensing:

The computer code and data files described and made available on this web page are distributed under the MIT license

Languages:

biharmonic_fd1d is available in a MATLAB version and an Octave version.

Related Data and Programs:

biharmonic_fd1d_test

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Source Code:


Last revised on 12 June 2023.