A numerical method for solving some nonlinear problems

Details A numerical method for solving some nonlinear problems A numerical method for solving some nonlinear problems

2000-10-02

arxiv.org/abs/math-ph/0010004v1

Math Models and Meth. in Appl Sciences, 9, N2, (1999), 325-335

Physics

Mathematical Physics

Scientific paper

A nonlinear equation in a Banach space is written as a linear equation with a linear operator depending on the unknown solution. This method, which we call a global linearization method, differs essentially from the local linearization methods of the Newton-type. Inverting the above linear operator by the methods known for linear operators one gets an equation which sometimes is much better for numerical solution than the original one. Some theorems about convergence of the proposed iterative process for solving the transformed equation are given. Examples of applications are considered.

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