Download or read book Variable Transformations for Difference Equations written by Tammy Marie Voepel and published by . This book was released on 1997 with total page 118 pages. Available in PDF, EPUB and Kindle. Book excerpt: Change of independent variable $t = 1/x$ motivates variable step size discretizations of even order differential operators. Hinton and Lewis performed a change of independent and dependent variables on second order differential operators in order to read off results for operators with singularities at zero from results previously known at infinity. In Chapter 2 we perform a similar change of variables on second order difference operators. The resulting identity can be used to read off oscillation and spectral theory results at zero from results previously known at infinity. In Chapter 3 we develop variable change methods for discrete symplectic (i.e., J-orthogonal) systems. This enables us to perform simultaneous change of independent and dependent variables on discrete linear Hamiltonian systems and on newly defined even order variable step size formally self adjoint difference operators. These variable changes yield a new system which is related to the original system by an operator identity. We generalize results of Bohner and Dosly on transformations of formally self adjoint scalar difference operators. They only considered a change of dependent variable whereas these methods allow $y(x\sb{n}) = \mu(x\sb{n})z(t\sb{n})$ where $t\sb{n} = f(x\sb{n}).$ These variable change results bring the subject of transformation theory for even order difference operators closer to the known transformation theory in the continuous case.