期刊
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
卷 43, 期 3, 页码 1380-1398出版社
WILEY
DOI: 10.1002/mma.5954
关键词
adams-bashforth rule; hermite interpolation; initial-value problems; interpolation; linear multi-step method; weighted hermite quadrature rule
资金
- Alexander von Humboldt Foundation [3.4 - IRN - 1128637]
- Agencia Estatal de Innovacion of Spain [MTM2016-75140-P]
- European Community Fund FEDER
- Xunta de Galicia [GRC 2015-004, R 2016/022]
In this paper, we first introduce a modification of linear multistep methods, which contain, in particular, the modified Adams-Bashforth methods for solving initial-value problems. The improved method is achieved by applying the Hermite quadrature rule instead of the Newton-Cotes quadrature formulas with equidistant nodes. The related coefficients of the method are then represented explicitly, the local error is given, and the order of the method is determined. If a numerical method is consistent and stable, then it is necessarily convergent. Moreover, a weighted type of the new method is introduced and proposed for solving a special case of the Cauchy problem for singular differential equations. Finally, several numerical examples and graphical representations are also given and compared.
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