In this paper, we show that some functions related to the dual Simpson’s formula and Bullen- Simpson’s formula are Schur-convex provided that f is four-convex. These results should be compared to that of Simpson’s ...In this paper, we show that some functions related to the dual Simpson’s formula and Bullen- Simpson’s formula are Schur-convex provided that f is four-convex. These results should be compared to that of Simpson’s formula in Applied Math. Lett. (24) (2011), 1565-1568.展开更多
The programs offered for solving nonlinear equations, usually the old method, such as alpha, chordal movement, Newton, etc. have been used. Among these methods may Newton’s method of them all be better and higher int...The programs offered for solving nonlinear equations, usually the old method, such as alpha, chordal movement, Newton, etc. have been used. Among these methods may Newton’s method of them all be better and higher integration. In this paper, we propose the integration method for finding the roots of nonlinear equation we use. In this way, Newton’s method uses integration methods to obtain. In previous work, [1] and [2] presented numerical integration methods such as integration, trapezoidal and rectangular integration method that are used. The new method proposed here, uses Simpson’s integration. With this method, the approximation error is reduced. The calculated results show that this hypothesis is confirmed.展开更多
Following a six-step flow chart, exponentially-fitted variant of the 2-step Simpson’s method suitable for solving ordinary differential equations with periodic/oscillatory behaviour is constructed. The qualitative pr...Following a six-step flow chart, exponentially-fitted variant of the 2-step Simpson’s method suitable for solving ordinary differential equations with periodic/oscillatory behaviour is constructed. The qualitative properties of the constructed methods are also investigated. Numerical experiments on standard problems confirming the theoretical expectations regarding the constructed methods compared with other existing standard methods are also presented. Our results unify and improve the existing classical 2-step Simpson’s method.展开更多
文摘In this paper, we show that some functions related to the dual Simpson’s formula and Bullen- Simpson’s formula are Schur-convex provided that f is four-convex. These results should be compared to that of Simpson’s formula in Applied Math. Lett. (24) (2011), 1565-1568.
文摘The programs offered for solving nonlinear equations, usually the old method, such as alpha, chordal movement, Newton, etc. have been used. Among these methods may Newton’s method of them all be better and higher integration. In this paper, we propose the integration method for finding the roots of nonlinear equation we use. In this way, Newton’s method uses integration methods to obtain. In previous work, [1] and [2] presented numerical integration methods such as integration, trapezoidal and rectangular integration method that are used. The new method proposed here, uses Simpson’s integration. With this method, the approximation error is reduced. The calculated results show that this hypothesis is confirmed.
文摘Following a six-step flow chart, exponentially-fitted variant of the 2-step Simpson’s method suitable for solving ordinary differential equations with periodic/oscillatory behaviour is constructed. The qualitative properties of the constructed methods are also investigated. Numerical experiments on standard problems confirming the theoretical expectations regarding the constructed methods compared with other existing standard methods are also presented. Our results unify and improve the existing classical 2-step Simpson’s method.
