Diamanlab

Diamanlab - An interactive Taylor-based continuation tool in MATLAB. With the interactive continuation tool Diamanlab, solution branches of a parametric nonlinear problem are computed as sets of Taylor-based solutions stored in checkpoints. Theoretical aspects and implementation are generic, taking advantage of the efficient higher-order asymptotic numerical method in its Diamant form that interprets the generic nonlinear problem as a sequence of linear ones, of Automatic Differentiation (AD) for Taylor coefficient computations, of object-oriented programming and graphical user interface capabilities of MATLAB. The implementation involves four classes devoted to the interactive management of the continuation, to the manipulation of a generic system of nonlinear equations, to the checkpoint management and to higher-order AD, respectively. In practice, any analytical nonlinear system of equation may be implemented in a natural way as a subclass of the generic system class, then solved in an easy manner using the graphical user interface. A benchmark of classical nonlinear problems is provided to serve as a basis for the implementation userdefined problems. Diamanlab usage and bifurcation detection are discussed on the Brusselator problem whose solution involves three interconnected loops. Additional user-defined graphics are presented for the Bratu problem.