by Shuping Chen and Youhua Qian
Original Research
In this article we construct some higher-order modifications of Newton’s method for solving nonlinear equations, which is based on the undetermined coefficients. This construction can be applied to any iteration formula. It can be found that per iteration the resulting methods add only one additional function evaluation, their order of convergence can be increased by two or three units. Higher order convergence of our methods is proved and corresponding asymptotic error constants are expressed. Numerical examples, obtained using Matlab with high precision arithmetic, are shown to demonstrate the convergence and efficiency of the combined iterative methods. It is found that the combined iterative methods produce very good results on tested examples, compared to the results produced by the existing higher order schemes in the related literature.
American Journal of Applied Mathematics and Statistics. 2017, 5(1), 22-32. DOI: 10.12691/ajams-5-1-5
Pub. Date: April 06, 2017
10416 Views2755 Downloads
by Hassan Ghassemi and Alireza Ahani
Original Research
This paper deals with solving the quantity element using new numerical techniques on discontinues boundary element method (DBEM). The common practice in getting solution with BEM is using constant element and for that, in a Sub-parametric element, quantity has a constant value along the element and geometry discretization is supposed to have a linear variation. But using higher order (polynomial) distribution of quantity over elements could have a better description of physical process. For this, the corresponding discretized expressions based on new techniques are derived and used for solution of Laplace equation. Many results for the quantity elements are presented and discussed for the ellipse at various diameters and mesh numbers.
American Journal of Applied Mathematics and Statistics. 2017, 5(1), 14-21. DOI: 10.12691/ajams-5-1-4
Pub. Date: March 30, 2017
10714 Views2059 Downloads
by Neelam Pandey and Ashiq Hussain Khan
Original Research
In the present paper, the author establish new unified integral whose integral contains products of H-function of several complex variable [1] and a general polynomials given by Srivastava [2] with general arguments. A large number of integrals involving various simpler functions follow as special cases of this integral.
American Journal of Applied Mathematics and Statistics. 2017, 5(1), 11-13. DOI: 10.12691/ajams-5-1-3
Pub. Date: February 18, 2017
8340 Views2021 Downloads6 Likes
by K. Prudhvi
Original Research
In this paper, we prove fixed point theorems on c-distance in ordered cone metric spaces. Our results are generalize, improve and extension of the recent work existing in the literature.
American Journal of Applied Mathematics and Statistics. 2017, 5(1), 8-10. DOI: 10.12691/ajams-5-1-2
Pub. Date: January 22, 2017
8332 Views2136 Downloads10 Likes
by Nick Z. Zacharis
Original Research
Inspired by the method of undetermined coefficients, this paper presents an alternative method to solve linear differential equations with constant coefficients, using the technique of polynomial long division. Expanding this technique with the exponential shift law enables to solve all types of non-homogeneous differential equations, of where the undetermined coefficients can be applied.
American Journal of Applied Mathematics and Statistics. 2017, 5(1), 1-7. DOI: 10.12691/ajams-5-1-1
Pub. Date: January 13, 2017
8942 Views1839 Downloads5 Likes