Petrov-Galerkin methods for nonlinear systems without monotonicity

Yuan Ming Wang; Ben Yu Guo

doi:10.1016/S0168-9274(99)00054-9

Petrov-Galerkin methods for nonlinear systems without monotonicity

Yuan Ming Wang
, Ben Yu Guo

School of Mathematical Sciences

Shanghai Normal University

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

Petrov-Galerkin method is investigated for solving nonlinear systems without monotonicity. A new concept of ordered pair of supersolution and subsolution is proposed. The existence of numerical solutions is studied. A new monotone iteration is provided for solving the resulting problem. Two conditions are given, ensuring the geometric convergence rate. The numerical results show the advantages of this method.

Original language	English
Pages (from-to)	57-78
Number of pages	22
Journal	Applied Numerical Mathematics
Volume	36
Issue number	1
DOIs	https://doi.org/10.1016/S0168-9274(99)00054-9
State	Published - Jan 2001

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title = "Petrov-Galerkin methods for nonlinear systems without monotonicity",

abstract = "Petrov-Galerkin method is investigated for solving nonlinear systems without monotonicity. A new concept of ordered pair of supersolution and subsolution is proposed. The existence of numerical solutions is studied. A new monotone iteration is provided for solving the resulting problem. Two conditions are given, ensuring the geometric convergence rate. The numerical results show the advantages of this method.",

author = "Wang, \{Yuan Ming\} and Guo, \{Ben Yu\}",

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AU - Guo, Ben Yu

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AB - Petrov-Galerkin method is investigated for solving nonlinear systems without monotonicity. A new concept of ordered pair of supersolution and subsolution is proposed. The existence of numerical solutions is studied. A new monotone iteration is provided for solving the resulting problem. Two conditions are given, ensuring the geometric convergence rate. The numerical results show the advantages of this method.

UR - https://www.scopus.com/pages/publications/0035149226

U2 - 10.1016/S0168-9274(99)00054-9

DO - 10.1016/S0168-9274(99)00054-9

M3 - 文章

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VL - 36

SP - 57

EP - 78

JO - Applied Numerical Mathematics

JF - Applied Numerical Mathematics

IS - 1

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Petrov-Galerkin methods for nonlinear systems without monotonicity

Abstract

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