A mesh independence principle for nonlinear equations using newton's method ano nonlinear projections.

• Autores: Ioannis K. Argyros
• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 8, Nº. 16, 1990, págs. 48-63
• Idioma: inglés
• DOI: 10.22199/S07160917.1990.0016.00004
• Enlaces
  • Texto completo
• Resumen

  • 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.

• Referencias bibliográficas
  • Citas ALLGOWER, E.L. and McCORMICK, S.F. Newton's method with mesh refinements for numerical solution of nonlinear two-point boundary...
  • ALLGOWER, E.L., McCORMICK, S.F. and PRYOR, D.V. A general mesh independence principle for Newton's method applied to second order boundary...
  • ALLGOWER, E.L., BOHMER, K., POTRA, F.A. and RHEINBOLDT, W.C. A mesh independence principle for operator equations and their discretizations....
  • ARGYROS, I.K. Quadratic equations and applications to Chandrasekhar's and related equations. Bull. Austral. Math. Soc. Vol. 32 (1985),...
  • McCORMICK, S.F. A revised mesh reforcement strategy for Newton's method applied to nonlinear two-point boundary value problems. Lecture...
  • ORTEGA, J.M. and RHEINBOLDT, W.C. On discretization and differentiation of operators with application to Newton's method. SIAM J. Num....
  • ___: 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....