Original Research Article

TWO-STEP INTEGRAL COLLOCATION-VARIATIONAL ITERATION METHOD FOR THE SOLUTIONS OF INTEGRO-DIFFERENTIAL EQUATIONS

A. O. ADEWUMI, O. M. OGUNLARAN, R. A. RAJI

Asian Journal of Mathematics and Computer Research, Page 379-387

In this paper, an algorithm based on integral collocation and variational iteration method for solving integro-differential equations is presented. In the rst instance, integro-differential equations are reduced to a system of integral equations after which we replaced all the derivatives in the new system of integral equations with their equivalent new derivatives. These new derivatives were obtained by approximating the nth order derivative with truncated Chebyshev series and then integrated n-times to obtain expressions for lower-order derivatives and the function itself. After the second iteration, the residual equation is formed which is collocated at the chosen collocation points and extra n equations are also obtained from the boundary conditions. Computational results are given for test examples to demonstrate the effectiveness, reliability, applicability and efficiency of the new method. It is shown that the solutions obtained from the method have very high degree of accuracy.

Original Research Article

A SIMPLE AND EFFICIENT ROOT-FINDING ALGORITHM FOR DEALING WITH SCALAR NONLINEAR EQUATIONS: ITERATIVE PROCEDURE BASED ON GEOMETRIC CONSIDERATIONS

GREGORY ANTONI

Asian Journal of Mathematics and Computer Research, Page 388-412

In this study, we present a simple and efficient root-finding algorithm for approximating the solution of scalar nonlinear equations. The proposed iterative scheme is based on geometric considerations using only the first-order derivative associated with the nonlinear function in question. The predictive capabilities of this numerical procedure for providing an accurate approximate solution associated with a nonlinear equation are tested, assessed and discussed on some examples.

Original Research Article

A GEOMETRY-BASED ITERATIVE ALGORITHM FOR FINDING THE APPROXIMATE SOLUTIONS OF SYSTEMS OF NONLINEAR EQUATIONS

GREGORY ANTONI

Asian Journal of Mathematics and Computer Research, Page 413-431

This paper is devoted to a new iterative method for finding the approximate solutions of systems of nonlinear equations. Based on some geometric considerations, a root-finding algorithm applied to a single equation is developed and coupled with Jacobi and Gauss-Seidel procedures with the aim of solving nonlinear systems. The numerical predictive abilities of this iterative method are addressed and discussed on some examples.

Original Research Article

FIXED POINT RESULTS ON A CLOSED BALL IN K-SEQUENTIALLY-COMPLETE PREORDERED QUASI-PARTIAL METRIC SPACES

ABDULLAH SHOAIB, MUHAMMAD ARSHAD, FAHIMUDDIN .

Asian Journal of Mathematics and Computer Research, Page 432-440

Fixed point results for the self dominated mappings satisfying locally Hardy Roger type contractive conditions on a closed ball in K-sequentially 0-complete preordered quasi-partial metric space have been established. An example has been given. Many well-known recent results have been generalized.

Original Research Article

FORCING ROMAN DOMINATION IN GRAPHS

P. ROUSHINI LEELY PUSHPAM, S. PADMAPRIEA

Asian Journal of Mathematics and Computer Research, Page 441-453

A set S of vertices is a dominating set if every vertex in V \ S has a neighbour in S. A Roman dominating function (RDF) on a graph G = (V,E) is defined to be a function f : V → {0, 1, 2} satisfying the condition that every vertex u for which f(u) = 0 is adjacent to at least one vertex v for which f(v) = 2. A Roman dominating function f of G can also be represented by a set of ordered pairs Sf = {(v, f(v)) : v V } . A subset T of Sf is called a forcing subset of Sf if Sf is the unique extension of T to a γR(G)-function. We define a forcing Roman domination number of Sf denoted by F(Sf, γR), as F(Sf, R) = min{|T| : T is aforcing subset of Sf }. The forcing Roman domination number F(G, γR) of G is degined as F(G; γR) = min{f(Sf, γR) : f is a γR(G) function}. Hence for every graph G, F(G,γR) 0. In this paper, we initiate a study of this parameter. We also obtain the forcing Roman domination number of paths, cycles, complete graphs, and complete multipartite

graph.