AWERProcedia Information Technology & Computer Science 1 (2012) 1111-1119 2 nd World Conference on Information Technology (WCIT-2011) Hermite cubic spline wavelet approximation for two point boundary value problems Mehdi Yousefi a * , Hesamoddin Derili Gherjalar a , Asghar Arzhang a a Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran Abstract In this paper, we use the wavelet bases of Hermite cubic splines to solve the linear two point boundary value problems. Two test problems are presented and numerical results are tabulated to show the efficiency of the proposed technique for the studied problem. For stability of the proposed method, we prove that the corresponding stiffness matrix arises from the discretization of the problem is sparse and the condition number of this matrix is uniformly bounded. Keywords: Boundary Value Problem, Wavelet, Approximation, Spline, Condition number; Selection and peer review under responsibility of Prof. Dr. Hafize Keser. ©2012 Academic World Education & Research Center. All rights reserved. 2. Introduction Wavelets have been applied recently to obtain representations of integral and differential operators in many physical problems. Wavelets have the multi-resolution analysis (MRA) property [1-3]. In recent years, the application of methods based on spline wavelets have influence on many areas of applied mathematics. Spline wavelets are used as a powerful tool in the numerical analysis of differential and integral equations [4-6]. In section 2, we will introduce wavelets of Hermite cubic splines and briefly recall the basic ideas. In sections 3 and 4 we will apply the wavelets for numerical solutions of the two point boundary value problems with the Dirichlet boundary condition. The corresponding stiffness matrix arises from the discretization of the problem is sparse and the condition number of this matrix is uniformly bounded (independent of the number of bases functions). *ADDRESS FOR CORRESPONDENCE; Mehdi, Yousefi, Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran E-mail address: m -yousefi@kiau.ac.ir/ Tel.: +98-938-895-0057