Birkisson, Asgeir and Driscoll, Tobin A. (2010) Automatic Frechet differentiation for the numerical solution of boundaryvalue problems. Technical Report. ACM. (Submitted)

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Abstract
A new solver for nonlinear boundaryvalue problems (BVPs) in Matlab is presented, based on the Chebfun software system for representing functions and operators automatically as numerical objects. The solver implements Newton's method in function space, where instead of the usual Jacobian matrices, the derivatives involved are Frechet derivatives. A major novelty of this approach is the application of automatic differentiation (AD) techniques to compute the operatorvalued Frechet derivatives in the continuous context. Other novelties include the use of anonymous functions and numbering of each variable to enable a recursive, delayed evaluation of derivatives with forward mode AD. The AD techniques are applied within a new Chebfun class called chebop which allows users to set up and solve nonlinear BVPs in a few lines of code, using the "nonlinear backslash" operator (. This framework enables one to study the behaviour of Newton's method in function space.
Item Type:  Technical Report (Technical Report) 

Subjects:  H  N > Numerical analysis 
Research Groups:  Numerical Analysis Group 
ID Code:  1023 
Deposited By:  Lotti Ekert 
Deposited On:  30 Nov 2010 07:13 
Last Modified:  29 May 2015 18:42 
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