Hermite wavelet based galerkin method for the numerical solutions of one dimensional elliptic problems

Abstract

1 Department of Mathematics, Karnatak University Dharwad-580003, India 2 Department of Mathematics, Govt. First Grade College, Chikodi \u2013 591201, India (Received September 03 2018, accepted November 21 2018) Abstract \u00a0 Wavelet analysis is a recently developed mathematical tool in applied mathematics. \u00a0In this paper, we proposed the wavelet based Galerkin method for the numerical solution of one dimensional elliptic problems using Hermite wavelets. \u00a0Here, Galerkin bases are constructed Hermite functions which are orthonormal bases and these are assumed bases elements which allow us to obtain the numerical solutions of the elliptic problems. \u00a0The obtained numerical solutions are compared with the existing numerical methods and exact solution. Some of the test problems are considered to demonstrate the applicability and validity of the purposed method. \u00a0