Nonlinear hyperbolic partial differential and Volterra integral equations: Analytical and numerical approaches (Q2754444)

The authors employ linear hyperbolic partial differential and Volterra integral inequalities to solve nonlinear characteristic hyperbolic initial-boundary value problems and Volterra integral equations. Three types of monotone iterative schemes are presented: (i) the alternating sequence scheme; (ii) the monotone iterative scheme; and (iii) generalized quasilinear scheme. The iteration in all these schemes are linear and hence, is easily computable by using the variation of parameters formulas and the resolvent kernel techniques. Whereas the mode of convergence of the iteration in the first two schemes is linear, that in the third scheme is quadratic and hence, more rapid. Numerical examples are given in support of the analytical methods.NEWLINENEWLINEFor the entire collection see [Zbl 0961.00018].