Particular Solutions of Ordinary Differential Equations Using Discrete Symmetry Groups

Symmetry Groups and Group Invariant Solutions of Partial Differential Equations

Bounds for Solutions of Ordinary Differential Equations

1. An upper bound for the norm of a system of ordinary differential equations can be obtained by comparison with a related first order differential equation, [4; 8]. This first order equation depends on an upper bound for the norm of the right side of the system. Recently, it has been pointed out [l; 6] that this same upper bound also gives a lower bound for the norm of the solution in terms of...

Wavelet Galerkin Solutions of Ordinary Differential Equations

Abstract. Advantage of wavelet Galerkin method over finite difference or element method has led to tremendous applications in science and engineering. In recent years there has been increasing attempt to find solutions of differential equations using wavelet techniques. In this paper, we elaborate the wavelet techniques and apply Galerkin procedure to analyse one dimensional harmonic wave equat...

New solutions for ordinary differential equations

This paper introduces a new method for solving ordinary differential equations (ODEs) that enhances existing methods that are primarily based on finding integrating factors and/or point symmetries. The starting point of the new method is to find a non-invertible mapping that maps a given ODE to a related higher-order ODE that has an easily obtained integrating factor. As a consequence, the rela...

Solving Differential Equations by Symmetry Groups

respectively. In an elementary course in differential equations, we learn that equations of the form dy/dx = f(x)g(y) are separable and are simple to solve because we can separate terms involving only x from those involving only y = y(x). In fact, as we will see, the deeper property that lets us solve these is the presence of a Lie group symmetry: a continuous transformation that takes each sol...