GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems
SIAM Journal on Scientific and Statistical Computing
Accuracy Enhancement for Higher Derivatives using Chebyshev Collocation and a Mapping Technique
SIAM Journal on Scientific Computing
ISSAC '97 Proceedings of the 1997 international symposium on Symbolic and algebraic computation
A BVP solver based on residual control and the Maltab PSE
ACM Transactions on Mathematical Software (TOMS)
On the Role of Natural Level Functions to Achieve Global Convergence for Damped Newton Methods
Proceedings of the 19th IFIP TC7 Conference on System Modelling and Optimization: Methods, Theory and Applications
SCAM '02 Proceedings of the Second IEEE International Workshop on Source Code Analysis and Manipulation
Introduction to Numerical Continuation Methods
Introduction to Numerical Continuation Methods
Using AD to solve BVPs in MATLAB
ACM Transactions on Mathematical Software (TOMS)
An efficient overloaded implementation of forward mode automatic differentiation in MATLAB
ACM Transactions on Mathematical Software (TOMS)
Evaluating Derivatives: Principles and Techniques of Algorithmic Differentiation
Evaluating Derivatives: Principles and Techniques of Algorithmic Differentiation
Newton Methods for Nonlinear Problems: Affine Invariance and Adaptive Algorithms
Newton Methods for Nonlinear Problems: Affine Invariance and Adaptive Algorithms
Source transformation for MATLAB automatic differentiation
ICCS'06 Proceedings of the 6th international conference on Computational Science - Volume Part IV
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A new solver for nonlinear boundary-value 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 Fréchet derivatives. A major novelty of this approach is the application of automatic differentiation (AD) techniques to compute the operator-valued Fréchet 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 which allows users to set up and solve nonlinear BVPs, both scalar and systems of coupled equations, 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.