www.tjprc.org editor@tjprc.org International Journal of Mathematics and Computer Applications Research (IJMCAR) ISSN(P): 2249-6955; ISSN(E): 2249-8060 Vol. 4, Issue 6, Dec 2014, 17-26 © TJPRC Pvt. Ltd. AN EFFICIENT METHOD OF BOUNDED SOLUTION OF A SYSTEM OF DIFFERENTIAL EQUATIONS USING LINEAR LEGENDRE MULTIWAVELETS MEENU DEVI 1 , S. R. VERMA 2 & M. P. SINGH 3 Department of Mathematics and Statistics, Faculty of Science, Gurukula Kangri University, Haridwar, Uttarkhand, India ABSTRACT In this paper, a method for the solution of the system of homogeneous linear differential equations with initial conditions by using Linear Legendre Multi wavelets is proposed. The Orthonormality and high vanishing moment properties of Linear Legendre Multi wavelets are used to find out an efficient, accurate and bounded solution for the system. Finally numerical results and exact solutions are compared by tables and graphs for two examples. KEYWORDS: System of Differential Equations, Legendre Multi Wavelets, Operational Matrix of Integration, Approximation Methods MSC2010: 33C45; 34K28; 42C10; 42C40; 65L80; 65T60 1. INTRODUCTION Wavelet permits the perfect representation of variety of functions and operators. Moreover, wavelets established a connection with fast numerical algorithms [1]. The advantage of Multi wavelets, as extensions from scalar wavelets and their confident features have resulted in an increase way to study them. Features such as orthogonality, compact support, symmetry, higher-order vanishing moments and the simple structure make Multi wavelets valuable both in theory and applications [2-5]. In recent years, several methods have been used to solve many systems such as lumped and distributed-parameter system [6], system of integro-differential equations [7-9], time-varying system [10], state-space system [11], optimal control time-delayed system [12-13] etc. In this paper, the system of homogeneous linear differential equations through Linear Legendre Multi wavelet (LLMW) bases on [0, 1] is discussed. The importance of applying Linear Legendre Multi wavelets is that it reduces the problems to solving a set of linear algebraic equations by truncated approximation series [14-17]. In the section 2, introduce Linear Legendre Multi wavelet (LLMW) and a method for solving the system of homogeneous linear differential equations is developed and the theorem on the bound of approximate solution of the system of differential equations is presented in section 3. Finally two examples are solved by the present method and obtained the approximate solution in section 4. 2. LINEAR LEGENDRE MULTIWAVELETS We can define a wavelet [3] on a family of functions constructed from translation and dilation of a single function as: