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approximations; inverse mapping; error bounds; Banach space; matrix differential equations; one-step-method; numerical example
In this paper we propose a procedure to construct approximations of the inverse of a class of ${\mathcal C}^{m}$ differentiable mappings. First of all we determine in terms of the data a neighbourhood where the inverse mapping is well defined. Then it is proved that the theoretical inverse can be expressed in terms of the solution of a differential equation depending on parameters. Finally, using one-step matrix methods we construct approximate inverse mappings of a prescribed accuracy.
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