biharmonic_fd2d

biharmonic_fd2d, a MATLAB code which deals with the biharmonic equation in two dimensions, whose simplest form is uxxxx + 2uxxyy + uyyyy = f.

Licensing:

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

Languages:

biharmonic_fd2d is available in a MATLAB version.

Related Data and Programs:

biharmonic_fd2d_test

biharmonic_cheby1d, a MATLAB code which uses Chebyshev methods to solve the biharmonic equation over an interval, a fourth order two point boundary value problem (BVP) in one spatial dimension.

biharmonic_fd1d, a MATLAB 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.

Reference:

1. Louis Ehrlich, Murli Gupta,
   Some difference schemes for the biharmonic equation,
   SIAM Journal on Numerical Analysis,
   Volume 12, Number 5, October 1975, pages 773-790.
2. Lloyd Trefethen,
   Spectral methods in MATLAB,
   SIAM, 2000,
   ISBN: 0898714656,
   LC: QA377.T65.

Source Code:

• biharmonic_fd2d_derivative.m, evaluates the derivatives of the biharmonic equation.
• biharmonic_fd2d_parameters.m, set or get parameters for the test cases.
• biharmonic_fd2d_rhs.m, evaluates the right hand side function f(x,y) for the test cases.
• biharmonic_fd2d_solution.m, evaluates the exact solution for the test cases.
• biharmonic_fd2d_stencil.m, defines a 5x5 matrix that implements a finite difference stencil for the biharmonic operator.
• rms.m, returns the root-mean-square norm of a vector or matrix.