Nonlinear equation solvers in boundary value problem codes
In this paper, the state-of-the-art of solving NLEQs arising in BVP codes has been surveyed. One of the essentials was to point out that the structure of the underlying BVP should be transparent in the selected realization of the NLEQ algorithm. A second point was to emphasize the importance of affine invariant techniques in the numerical treatment of highly nonlinear real life problems. For this reason and for lack of space, NLEQ solvers different from Newton's method were omitted in this presentation. However, a thorough comparison of different NLEQ algorithms implemented in each BVP code is still lacking. Such a comparison, which would have been beyond the scope of this paper, should be based on a set of real life BVPs, in order to permit a comparative judgment of the different NLEQ solvers in BVP codes.
KeywordsMultiple Shooting Continuation Method Monotonicity Test Taylor Series Method Deferred Correction
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