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
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
Information collection from remote location is very important for several tasks such as temperate monitoring, air quality investigation, and wartime surveillance. Wireless sensor network is the first choice to complet...Information collection from remote location is very important for several tasks such as temperate monitoring, air quality investigation, and wartime surveillance. Wireless sensor network is the first choice to complete these types of tasks. Basically, information prediction scheme is an important feature in any sensor nodes. The efficiency of the sensor network can be improved to large extent with a suitable information prediction scheme. Previously, there were several efforts to resolve this problem, but their accuracy is decreased as the prediction threshold reduces to a small value. Our proposed Adams-Bashforth-Moulton algorithm to overcome this drawback was compared with the Milne Simpson scheme. The proposed algorithm is simulated on distributed sensor nodes where information is gathered from the Intel Berkeley Research Laboratory. To maximize the power saving in wireless sensor network, our adopted method achieves the accuracy of 60.28 and 59.2238 for prediction threshold of 0.01 for Milne Simpson and Adams-Bashforth-Moulton algorithms, respectively.展开更多
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.
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Information collection from remote location is very important for several tasks such as temperate monitoring, air quality investigation, and wartime surveillance. Wireless sensor network is the first choice to complete these types of tasks. Basically, information prediction scheme is an important feature in any sensor nodes. The efficiency of the sensor network can be improved to large extent with a suitable information prediction scheme. Previously, there were several efforts to resolve this problem, but their accuracy is decreased as the prediction threshold reduces to a small value. Our proposed Adams-Bashforth-Moulton algorithm to overcome this drawback was compared with the Milne Simpson scheme. The proposed algorithm is simulated on distributed sensor nodes where information is gathered from the Intel Berkeley Research Laboratory. To maximize the power saving in wireless sensor network, our adopted method achieves the accuracy of 60.28 and 59.2238 for prediction threshold of 0.01 for Milne Simpson and Adams-Bashforth-Moulton algorithms, respectively.
