Iterative methods for the darboux problem for partial functional differential equations

Tomasz Człapiński
1999 Journal of Inequalities and Applications  
We consider the Darboux problem for the hyperbolic partial functional differential equations (1) Dxyz(X, y) f(x, y, Z(x,y)), (x, y) where Z(x,y) a0, 0] x b0, 0] Z is a function defined by Z(x,y)(t, s) z(x + t, y + s), (t, s) a ao, 0] x bo, 0]. If X I then using the method of functional differential inequalities we prove, under suitable conditions, a theorem on the convergence of the Chaplyghin sequences to the solution of problem (1), (2). In case X is any Banach space we give analogous theorem
more » ... e analogous theorem on the convergence of the Newton method.
doi:10.1155/s1025583499000338 fatcat:6636yl3jnzaoricnrdgu6zeg74