http://repo.lib.jfn.ac.lk/ujrr/handle/123456789/130 2026-04-16T10:23:10Z http://repo.lib.jfn.ac.lk/ujrr/handle/123456789/9559 Title: On the convergence of the accelerated Riccati iteration method Authors: Prasanthan, R.; Jianhong Xu Abstract: In this paper, we establish results fully addressing two open problems proposed recently by I. Ivanov, see Nonlinear Analysis 69 (2008) 4012–4024, with respect to the convergence of the accelerated Riccati iteration methodfor solving the continuous coupled algebraic Riccati equation, or CCAREfor short. These results confirm several desirable features of that method, including the monotonicity and boundedness of the sequences it produces, its capability of determining whether the CCARE has a solution, the extremal solutions it computes under certain circumstances, and its faster convergence than the regular Riccati iteration method 2020-01-01T00:00:00Z http://repo.lib.jfn.ac.lk/ujrr/handle/123456789/9543 Title: Analysis of the Convergence of More General Linear Iteration Scheme on the Implementation of Implicit Runge-Kutta Methods to Stiff Differential Equations Authors: Vigneswaran, R.; Kajanthan, S. Abstract: A modified Newton scheme is typically used to solve large sets of non-linear equations arising in the implementation of implicit Runge-Kutta methods. As an alternative to this scheme, iteration schemes, which sacrifice superlinear convergence for reduced linear algebra costs, have been proposed. A more general linear iterative scheme of this type proposed by Cooper and Butcher in 1983 for implicit Runge-Kutta methods, and he has applied the successive over relaxation technique to improve the convergence rate. In this paper, we establish the convergence result of this scheme by proving some theoretical results suitable for stiff problems. Also these convergence results are verified by two and three stage Gauss method and Radue IIA method. 2020-01-01T00:00:00Z http://repo.lib.jfn.ac.lk/ujrr/handle/123456789/9542 Title: Solitary wave solutions of the Camassa–Holm-Nonlinear Schrödinger Equation Authors: Mathanaranjan, T. Abstract: This study investigates the solitary wave solutions to the defocusing nonlinear Schrödinger equation, which is known as Camassa–Holm-Nonlinear Schrödinger (CH-NLS) equation. The CH-NLS equation is newly derived in the sense of deformation of hierarchies structure of integrable systems. By implementing three different techniques, namely, the generalized (𝐺′∕𝐺)-expansion method, the new mapping method, and the modified simple equation method, the CH-NLS equation is solved analytically to find the exact solutions. As a result, various types of solitons such as dark, singular, and periodic solutions are obtained. The behaviors of some exact solutions are presented by figures. 2020-01-01T00:00:00Z http://repo.lib.jfn.ac.lk/ujrr/handle/123456789/9325 Title: Some Behavior of Coarse structure and Coarse equivalence Authors: Kajan, N.; Kannan, K. Abstract: I am going to introduce some properties of coarse structure. Coarse space is defined for large scale in metric space similar to the tools provided by topology for analyzing behavior at small distance, as topological property can be defined entirely in terms of open sets. Analogously a large scale property can be defined entirely in terms of controlled sets. The properties we required were that the maps were coarse (proper and bornologous), but why do these maps imply that the spaces have the same large structure? Essentially this has to do with contractibility. Spaces which are the same on a large scale can be scaled so that the points are not too far away from each other, but we are not concerned with any differences on small scale that may arise. In addition I am going to explain some basic definition related with the title of my research work besides ,I want to investigate several results in coarse map, coarse equivalent and coarse embedding. Further I have to proof some results of product of coarse structure. Coarse map need not be a continuous map. Coarse space has some applica tion in various parts in mathematics. More over coarse structure is a large scale property so we can invest some results related with coarse space and topology. Topology is the small scale structure, but topological coarse structure is the large scale structure. We investigated some results about coarse maps, coarse equivalent and coarse embedding. 2020-01-01T00:00:00Z