Journal of Applied & Computational Mathematics

In this paper, we propose a numerical method to solve the nonlinear integral equation of the second kind. We intend to approximate the solution of this equation by Adomian decomposition method using He’s polynomials. Several examples are given at the end of this paper with the exact solution is known. Also the error is estimated.

 Let G={g1,…,gn} be an n-dimensional Chebyshev sub-space of C[a, b] such that 1∉G and U=(u0, u1 ,…,un ) be an (n+1)-dimensional subspace of C[a, b] where u0 =1, ui =gi , i=1….. n. Under certain restriction on G, we proved that U is a Chebyshev subspace if and only if it is a Weak Chebyshev subspace. In addition, some other related results are established.

 This research considers a symmetric hybrid continuous linear multistep method for the solution of general third order ordinary differential equations. The method is generated by interpolation and collocation approach using a combination of power series and exponential function as basis function. The approximate basis function is interpolated at both grid and off-grid points but the collocation of the differential function is only at the grid points. The derived method was found to be symmetric, consistent, zero stable and of order six with low error constant. Accuracy of the method was confirmed by implementing the method on linear and non-linear test problems. The results show better performance over known existing methods solved with the same third order problems. AMS 2010 Subject Classification: 65D05; 65L05; 65L06

 In the present paper, different Autoregressive Integrated Moving Average (ARIMA) models were developed to forecast the tea production by using time series data of twenty-four years from 1990-2013. The performance of these developed models was assessed with the help of different selection measure criteria and the model having minimum value of these criteria considered as the best forecasting model. Based on findings, it has been observed that out of eleven ARIMA models, ARIMA (1,1,2) is the best fitted model in predicting the production of tea in Bangladesh and the forecasted value of tea production in Bangladesh, for the year 2014, 2015 and 2016 as obtained from ARIMA (1,1,2) was obtained as 65.568 Million Kilogram, 67.867 Million Kilogram and 60.997 Million Kilogram.

 Basic notions related to the characterized fuzzy 1 2 2 R and characterized fuzzy 1 3 2 T -spaces are introduced and studied. The metrizable characterized fuzzy spaces are classified by the characterized fuzzy 1 2 2 R and the characterized fuzzy T4-spaces in our sense. The induced characterized fuzzy space is characterized by the characterized fuzzy 1 3 2 T and characterized fuzzy 1 3 2 T -space if and only if the related ordinary topological space is 1 2, 2 R ϕ 12 -space and 1 3, 2 T ϕ 12 -space, respectively. Moreover, the α-level and the initial characterized spaces are characterized 1 2 2 R and characterized 1 3 2 T -spaces if the related characterized fuzzy space is characterized fuzzy 12 2 R and characterized fuzzy 1 3 2 T , respectively. The categories of all characterized fuzzy 1 2 2 R and of all characterized fuzzy 1 3 2 T -spaces will be denoted by CFR-Space and CRF-Tych and they are concrete categories. These categories are full subcategories of the category CF-Space of all characterized fuzzy spaces, which are topological over the category SET of all subsets and hence all the initial and final lifts exist uniquely in CFR-Space and CRF-Tych. That is, all the initial and final characterized fuzzy 1 2 2 R spaces and all the initial and final characterized fuzzy 1 3 2 T -spaces exist in CFR-Space and in CRF-Tych. The initial and final characterized fuzzy spaces of a characterized fuzzy 1 2 2 R -space and of a characterized fuzzy 1 3 2 T -space are characterized fuzzy 1 2 2 R and characterized fuzzy 1 3 2 T -spaces, respectively. As special cases, the characterized fuzzy subspace, characterized fuzzy product space, characterized fuzzy quotient space and characterized fuzzy sum space of a characterized fuzzy 1 2 2 R -space and of a characterized fuzzy 1 3 2 T -space are also characterized fuzzy 1 2 2 R and characterized fuzzy 1 3 2 T -spaces, respectively. Finally, three finer characterized fuzzy 1 2 2 R -spaces and three finer characterized fuzzy 1 3 2 T -spaces are introduced and studied.

 This paper, presents three news-improved approximations to the Cumulative Distribution Function (C.D.F.). The first approximation improves the accuracy of approximation given by Polya (1945). In this first new approximation, we reduce the maximum absolute error (MAE) from0.000314 to 0.00103. For this first new approximation, Aludaat and Alodat were reduce the (MAE) from 0.000314 to 0.001972. The second new approximation improve Tocher’s approximation, we reduce the (MAE) from, 0.166 to 0.00577. For the third new approximation, we combined the two previous approximations. Hence, this combined approximation is more accurate and its inverse is hard to calculate. This third approximation reduces the (MAE) to be less than 2.232e-004. The two improved previous approximations are less accurate, but his inverse is easy to calculate. Finally, we give an application to the third approximation for pricing a European Call using Black-Scholes Model.

 In this paper, we present an iterative method to determine active point of linear constraints. It is based on two basic operations which are addition and permutation of constraints. This procedure generates a finite sequence of points that basis in a new lemma and a new formula direction, the laspoint of sequence constitutes an active point, and this procedure gives also two matrices. The first one is constituted by the active constraints which are linearly independent and the second one is a matrix whose columns are the basis vectors of the kernel of the first matrix. 

We propose the approximating sequence and some of characteristics of this sequence to coincide with the increments of the fractional Brownian motion (fractional Browniannoise) for the observed time series. We study the Hurst parameter estimation algorithm and check the quality of the approximation.

 In this paper, we present new type of 2D-volttera integrodifferential equations and study the existence, uniqueness and some other useful properties of solution of these equations. The main tools are based on application of the Banach fixed point theorem.

A new continuous numerical method based on the approximation of polynomials is here proposed for solving the equation arising from heat transfer along a thick steel slab and a hollow tube subject to initial and boundary conditions. The method results from discretization of the heat equation which leads to the production of a system of algebraic equations. By solving the system of algebraic equations we obtain the problem approximate solutions.