Authors:
H. S. Ramane; S.C. Shiralashetti, R. A. Mundewadi, R. B. Jummannaver Pages: 11 - 15 Abstract: The main purpose of this paper is to develop the graph theoretic polynomial to solve numerical problems. We present a new method for the solution of Fredholm integral equations using Hosoya polynomials obtained from one of the standard class of graphs called as path. Proposed algorithm expands the desired solution in terms of a set of continuous polynomials over a closed interval [0,1]. However, accuracy and efficiency are dependent on the size of the set of Hosoya polynomials and compared with the existing method. PubDate: 2018-1-9 DOI: 10.12691/ajna-5-1-2 Issue No:Vol. 5, No. 1 (2018)

Authors:
Gemechis File; Gashu Gadisa, Tesfaye Aga, Y. N. Reddy Pages: 1 - 10 Abstract: In this paper, we presented numerical method for solving singularly perturbed delay differential equations with layer or oscillatory behaviour for which a small shift (δ) is in the reaction term. First, the given singularly perturbed delay reaction-diffusion equation is converted into an asymptotically equivalent singularly perturbed two point boundary value problem and then solved by using fourth order finite difference method. The stability and convergence of the method has been investigated. The numerical results have been tabulated and further to examine the effect of delay on the boundary layer and oscillatory behavior of the solution, graphs have been given for different values of δ. Both theoretical and numerical rate of convergence have been established and are observed to be in agreement for the present method. Briefly, the present method improves the findings of some existing numerical methods in the literature. PubDate: 2017-2-5 DOI: 10.12691/ajna-5-1-1 Issue No:Vol. 5, No. 1 (2017)