Some modified Adams‐Bashforth methods based upon the weighted Hermite quadrature rules
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...
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| Veröffentlicht in: | Mathematical methods in the applied sciences 2020-02, Vol.43 (3), p.1380-1398 |
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| container_title | Mathematical methods in the applied sciences |
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| creator | Masjed‐Jamei, Mohammad Moalemi, Zahra Srivastava, Hari M. Area, Iván |
| description | 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. |
| doi_str_mv | 10.1002/mma.5954 |
| format | Article |
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| subjects | adams‐bashforth rule Cauchy problems Differential equations Graphical representations hermite interpolation initial‐value problems interpolation linear multi‐step method Methods Numerical methods Quadratures weighted hermite quadrature rule |
| title | Some modified Adams‐Bashforth methods based upon the weighted Hermite quadrature rules |
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