On the solution of a class of the reduced wave equation and the Riccati differential equation


Misir A.

APPLIED MATHEMATICS AND COMPUTATION, vol.216, no.5, pp.1375-1382, 2010 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Review
  • Volume: 216 Issue: 5
  • Publication Date: 2010
  • Doi Number: 10.1016/j.amc.2010.03.008
  • Title of Journal : APPLIED MATHEMATICS AND COMPUTATION
  • Page Numbers: pp.1375-1382
  • Keywords: Differential equation, Riccati differential equation, Acoustic scattering problem, Helmholtz equation, HELMHOLTZ-EQUATION

Abstract

In this paper we present an "iteration" technique for a class of differential equation having the form z '' = lambda z, where lambda is a function in C(infinity). We show that we can construct not only the general solution of the reduced wave equation but also the general solution of the Riccati differential equation by using this iteration technique if the given function lambda is satisfies the condition