A mesh independence principle for nonlinear equations using newton's method ano nonlinear projections.
DOI:
https://doi.org/10.22199/S07160917.1990.0016.00004Keywords:
Espacios dimensionales, Ecuaciones no linealesAbstract
We consider the nonlinear operator equation in a Banach space. We make use of nonlinear projections on finite dimensional spaces to produce the finite dimensional discretization of the nonlinear equation. Using Newton's method we then prove the mesh-independence principle for this problem. Our results cover and extend previous results involving linear projections on finite dimensional spaces.
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References
ALLGOWER, E.L. and McCORMICK, S.F. Newton's method with mesh refinements for numerical solution of nonlinear two-point boundary value problems. Numer. Math. 29 (1978), 237-260.
ALLGOWER, E.L., McCORMICK, S.F. and PRYOR, D.V. A general mesh independence principle for Newton's method applied to second order boundary value problems. Computing 23 (1979), 233-246.
ALLGOWER, E.L., BOHMER, K., POTRA, F.A. and RHEINBOLDT, W.C. A mesh independence principle for operator equations and their discretizations. SIAM J. Num. Anal. Vol. 23, 1, (1986), 160-169.
ARGYROS, I.K. Quadratic equations and applications to Chandrasekhar's and related equations. Bull. Austral. Math. Soc. Vol. 32 (1985), 275-292.
McCORMICK, S.F. A revised mesh reforcement strategy for Newton's method applied to nonlinear two-point boundary value problems. Lecture Notes in Mathematics 679, Springer-Verlag Publ. 1978, 15-23.
ORTEGA, J.M. and RHEINBOLDT, W.C. On discretization and differentiation of operators with application to Newton's method. SIAM J. Num. Anal. Vol. 3, (1966), 143-156.
___: Iterative solutions of nonlinear equations in several variables. Academic Press, New York, 1970.
RHEINBOLDT, W.C. An adaptive continuation process for solving systems of nonlinear equations. Polish Academy of Science. Banach Ctr. Publ. 3 (1977), 129-142.
ALLGOWER, E.L., McCORMICK, S.F. and PRYOR, D.V. A general mesh independence principle for Newton's method applied to second order boundary value problems. Computing 23 (1979), 233-246.
ALLGOWER, E.L., BOHMER, K., POTRA, F.A. and RHEINBOLDT, W.C. A mesh independence principle for operator equations and their discretizations. SIAM J. Num. Anal. Vol. 23, 1, (1986), 160-169.
ARGYROS, I.K. Quadratic equations and applications to Chandrasekhar's and related equations. Bull. Austral. Math. Soc. Vol. 32 (1985), 275-292.
McCORMICK, S.F. A revised mesh reforcement strategy for Newton's method applied to nonlinear two-point boundary value problems. Lecture Notes in Mathematics 679, Springer-Verlag Publ. 1978, 15-23.
ORTEGA, J.M. and RHEINBOLDT, W.C. On discretization and differentiation of operators with application to Newton's method. SIAM J. Num. Anal. Vol. 3, (1966), 143-156.
___: Iterative solutions of nonlinear equations in several variables. Academic Press, New York, 1970.
RHEINBOLDT, W.C. An adaptive continuation process for solving systems of nonlinear equations. Polish Academy of Science. Banach Ctr. Publ. 3 (1977), 129-142.
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2018-04-02
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How to Cite
[1]
“A mesh independence principle for nonlinear equations using newton’s method ano nonlinear projections”., Proyecciones (Antofagasta, On line), vol. 8, no. 16, pp. 48–63, Apr. 2018, doi: 10.22199/S07160917.1990.0016.00004.