Some Studies of Differential Equations by Operational Matrix Method and Haar Wavelet Approach

Abstract

The purpose of the work presented in this thesis is an effort to study some differential newlineand integral equations such as linear time-varying system, damped forced oscillator newlineproblems, homogeneous system of linear differential equations, Fredholm integral newlineequations and partially singularly perturbed system of initial and boundary value newlineproblems. To obtain the numerical solution of these differential and integral newlineequations, two approaches have been used in this thesis, namely, operational matrix newlinemethod and collocation method. The operational matrix method has been employed newlineusing three types of function approximations (i) Bernoulli othonormal polynomials, newline(ii) Haar wavelets and (iii) Linear Legendre multiwavelets. The collocation method newlinehas been used employing non-uniform Haar wavelet with different types of meshes. newlineAll the computations for numerical examples throughout the thesis have been done newlineusing software newline