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A parallel shooting technique for solving dissipative ODE’s. (English) Zbl 0788.65079
A new approach is presented designed for a restricted class of ordinary differential equations (ODE’s), where the righ-hand side function is dissipative. A fixed point problem arising from the application of a step-by-step method to a system of ODE’s is adopted. The authors’ formulation is based on the exact solution of the differential system. This new formulation is used to determine what kind of initial value problems should be considered.
A very simple algorithm aimed at solving the fixed point problem is introduced. Its convergence is studied in terms of the logarithmic norm of the right-hand-side. This algorithm already emphasizes the necessity of dealing only with a restricted class of problems. Newton’s method is considered. The class of dissipative problems is shown to be particulary appropriate. Numerical experiments aimed at verifying the theoretical convergence results for the proposed algorithm are presented.
The discrete-time version of the algorithm is studied. Especially the influence of the perturbations arising from the introduction of approximations is analyzed. Simulations are presented that prove of the proposed technique is competitive in situations, where it is not possible to parallelize “across the system”.
Reviewer: I.Dimov (Sofia)

MSC:
65L05 Numerical methods for initial value problems involving ordinary differential equations
65Y05 Parallel numerical computation
34A34 Nonlinear ordinary differential equations and systems
Software:
RODAS
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References:
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