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Application of global methods in parallel shooting. (English) Zbl 0801.65072

A new divide-and-conquer method is proposed to employ a coarse grid discretization like multiple shooting does, but to solve the local problems in a “boundary value problem-way”. A sophisticated error control is developed to combine local and global convergence of the Newton updating.

An implementation, called the unbiased multiple shooting algorithm by using the collocation code, is briefly discussed and a number of examples are given to illustrate the success of the method, in particular for singular perturbation problems. The method gives the possibility of making a stable parallel algorithm.

MSC:
65L10Boundary value problems for ODE (numerical methods)
65Y05Parallel computation (numerical methods)
34B15Nonlinear boundary value problems for ODE
34E15Asymptotic singular perturbations, general theory (ODE)
Software:
COLNEW