ABSTRACT
We shall consider, in this chapter, second-order hyperbolic differential equa tions which are natural generalizations of the equations studied in Chapter 4. As we are aware, the study of hyperbolic equations is of a different char acter compared with parabolic equations. Consequently, we shall provide, in Section 7.2, the appropriate notions and functional analytic framework that would facilitate the desired investigation of the methodology of monotone iterates and fast convergence. We shall also prove the required comparison principle using different ideas and tools. We shall extend, in Section 7.3 the monotone iterative technique for nonlinear hyperbolic IBVPs and in Section 7.4, the method of generalized quasilinearization. Both of these techniques are presented in a unified set-up so that several important special cases can be derived from them.
