Tridiagonal matrix algorithm

Abstract: Gaussian elimination is used in special linear groups to solve the word problem. In this paper, we extend Gaussian elimination to split unitary groups. These algorithms have an application in building a public-key cryptosystem, we demonstrate that.

Abstract: In this paper, a new numerical integration method on a uniform mesh is presented for the solution of singularly perturbed two-point boundary value problems having boundary layer at one end (left or right) point. The methods of Exact and Trapezoidal rule of integration with finite difference approximation of first derivatives are used to obtain a three-term recurrence relationship . The obtained tridiagonal system of equations is then solved using Thomas algorithm. Also, the stability and convergence of the proposed scheme are established. Several model example problems are solved using the proposed method. The results are presented in terms of maximum absolute errors which demonstrate the accuracy and efficiency of the method. It is observed that the proposed method is capable of producing highly accurate results with minimal computational effort for a fixed value of step size h, when perturbation parameter tends to zero.

Abstract: This paper presents a fitted fourth order numerical scheme for solving singularly perturbedconvection-diffusion equations. The obtained scheme is transformed into a three-term recurrence relation and solved by Thomas algorithm. The stability and convergence of thepresent method have been investigated. The numerical results are presented by tables and graphs. The present method helps us to get good results and also to know the behavior ofthe solution in the boundary layer for perturbation parameter e is less than mesh size h.Moreover, the present method improves the findings of some existing numerical methods reported in the literature.