జర్నల్ ఆఫ్ అప్లైడ్ & కంప్యూటేషనల్ మ్యాథమెటిక్స్

Analysis of the computational potential is provided for a modification of one of the numerical approaches to the classical boundary integral equations method. The originally proposed name of the approach is the method of functional equations, but in nowadays it is also referred to as the fundamental solutions method. Undesired after effects of this name flip are pointed out. The modification, implemented in this study, requires computer-friendly representations for some relevant Green's function and significantly enhances the resolving potential of the method. This work focuses on the exploration of the computational applicability of this modification. Chosen for that boundaryvalue problems and stated on regions of irregular configuration for second order elliptic equations with discontinuous coefficients.

In the present paper we study unique solvability of the analogues of problem Bitsadze for the degenerating hyperbolic-hyperbolic type equation. Uniqueness and existence theorem for solution of this problems are proven with principle extremum and by the method of integral equations.

We apply Nunokawa’s lemma, On Properties of Non-Carath´eodory Functions, Proc. Japan Acad. 68, Ser. A (1992) 152-153, to prove some new results.

The aim of this paper is to design neural network to present a method to solve Singular perturbation problems (SPP) by using network having one hidden layer with 5 hidden units (neurons) and one linear output unit, the sigmoid activation of each hidden units is tansigmoid. The neural network trained by the back propagation with different algorithms such as quasi-Newton, Levenberg-Marquardt, and Bayesian Regulation. Finally the results of numerical experiments are compared with the exact solution in illustrative examples to confirm the accuracy and efficiency of the presented scheme.

A stochastic, mathematical model known as a discrete Markov Chain was used to show how to estimate the probability that the mathematical achievement gap between African Americans and White Americans would close during a particular calendar year. The implications of race in the achievement of mathematics in the United States are profound and well-documented in mathematics education research literature. The authors used historical data drawn from the National Assessment of Educational Progress (NAEP) to examine trends of mathematical achievement between African Americans and White Americans during the assessment years of 1973–2012. The authors provide a discussion of NAEP data in the context of the discrete Markov Chain model and describe how specific properties of the Markov process were used to estimate the probability that the mathematical achievement gap will close within the next 50 years.

The purpose of this paper is that iteration scheme of multivalued non-expansive mappings in Banach spaces is extended to hyperbolic spaces and to prove some Δ−convergence theorems of the mixed type iteration process to approximating a common fixed point for two multivalued non-expansive mappings and two non-expansive mappings in hyperbolic spaces. The results presented in the paper extend and improve some recent results announced in the current literature.