Third-Order and Fourth-Order Iterative Methods Free from Second Derivative for Finding Multiple Roots of Nonlinear Equations

Abstract. In this paper, we present two new families of thirdorder and fourth-order methods for finding multiple roots of nonlinear equations. Each of them requires one evaluation of the function and two of its first derivative per iteration. Several numerical examples are given to illustrate the performance of the presented methods

Monthly variations of total lipids content and some biological parameters of rock oyster (Saccostrea cucullata) in the Northern coasts of the Gulf of Oman

The present study was conducted to assess the monthly variations of total lipids content and some biological parameters of rock oyster in the Northern coasts of the Gulf of Oman (Iranian coast) from October 2017 until March 2018 in relation to environmental conditions. According to the results, the maximum and minimum lengths were recorded in December and February, respectively. The highest amounts of weight, dry and wet weight, and condition index were recorded in autumn. There was also a significant difference between the months and the regions for these parameters (p < 0.05). The highest amount of total lipids was observed in March (3.1±1.84) with a significant difference relative to October and November and the lowest amount one was observed in October (2.15±1.6). Also, there was a significant relationship between the total lipids and the temperature. Moreover, there were higher amounts of total lipids in Saccostrea cucullata in winter compared to those in autumn. In general, one of the reasons for the differences in length, weight and total lipids at different stations over different months can mainly be explained by the reproduction season, nutritional conditions, and environmental factors such as temperature and salinity.

Monthly variations of total lipids content and some biological parameters of rock oyster (Saccostrea cucullata) in the Northern coasts of the Gulf of Oman

465-472The present study was conducted to assess the monthly variations of total lipids content and some biological parameters of rock oyster in the Northern coasts of the Gulf of Oman (Iranian coast) from October 2017 until March 2018 in relation to environmental conditions. According to the results, the maximum and minimum lengths were recorded in December and February, respectively. The highest amounts of weight, dry and wet weight, and condition index were recorded in autumn. There was also a significant difference between the months and the regions for these parameters (p < 0.05). The highest amount of total lipids was observed in March (3.1±1.84) with a significant difference relative to October and November and the lowest amount one was observed in October (2.15±1.6). Also, there was a significant relationship between the total lipids and the temperature. Moreover, there were higher amounts of total lipids in Saccostrea cucullata in winter compared to those in autumn. In general, one of the reasons for the differences in length, weight and total lipids at different stations over different months can mainly be explained by the reproduction season, nutritional conditions, and environmental factors such as temperature and salinity

Chebyshev cardinal functions for solving volterra-fredholm integro- differential equations using operational matrices

Abstract In this paper, an effective direct method to determine the numerical solution of linear and nonlinear Fredholm and Volterra integral and integro-differential equations is proposed. The method is based on expanding the required approximate solution as the elements of Chebyshev cardinal functions. The operational matrices for the integration and product of the Chebyshev cardinal functions are described in detail. These matrices play the important role of reducing an integral equation to a system of algebraic equations. Illustrative examples are shown, which confirms the validity and applicability of the presented technique

APPROXIMATE SOLUTION TO BOUNDARY VALUE PROBLEMS BY THE MODIFIED VIM

Abstract -This paper presents an efficient modification of the variational iteration method for solving boundary value problems using the chebyshev polynomials. The proposed method can be applied to linear and nonlinear models. The scheme is tested for some examples and the obtained results demonstrate the reliability and efficiency of the proposed method

Exponential Convergence for Numerical Solution of Integral Equations Using Radial Basis Functions

We solve some different type of Urysohn integral equations by using the radial basis functions. These types include the linear and nonlinear Fredholm, Volterra, and mixed Volterra-Fredholm integral equations. Our main aim is to investigate the rate of convergence to solve these equations using the radial basis functions which have normic structure that utilize approximation in higher dimensions. Of course, the use of this method often leads to ill-posed systems. Thus we propose an algorithm to improve the results. Numerical results show that this method leads to the exponential convergence for solving integral equations as it was already confirmed for partial and ordinary differential equations