The chebop system for automatic solution of differential equations
In MATLAB, it would be good to be able to solve a linear differential equation by typing <strong>u = L\\f</strong>, where <strong>f</strong>, <strong>u</strong>, and <strong>L</strong> are representations of the right-hand side, the solution, and the d...
| Main Authors: | , , |
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| Format: | Report |
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Oxford University Computing Laboratory
2008
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| Summary: | In MATLAB, it would be good to be able to solve a linear differential equation by typing <strong>u = L\\f</strong>, where <strong>f</strong>, <strong>u</strong>, and <strong>L</strong> are representations of the right-hand side, the solution, and the differential operator with boundary conditions. Similarly it would be good to be able to exponentiate an operator with <strong>expm(L)</strong> or determine eigenvalues and eigenfunctions with <strong>eigs(L)</strong>. A system is described in which such calculations are indeed possible, based on the previously developed chebfun system in object-oriented MATLAB. The algorithms involved amount to spectral collocation methods on Chebyshev grids of automatically determined resolution. |
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