G. Berikelashvili, O. Jokhadze, S. Kharibegashvili, and B. Midodashvili

Finite-Difference Method of Solving the Darboux Problem for the Nonlinear Klein-Gordon Equation

abstract:
The first Darboux problem for cubic nonlinear Klein-Gordon equation is considered, with a nonhomogeneous condition on the characteristic line. Solvability and convergence of the proper difference scheme is investigated in Sobolev spaces.

Mathematics Subject Classification: 26D10, 26D20, 34K10, 34K12

Key words and phrases: Gronwall type integral inequalities, hyperbolic partial differential equations, hyperbolic partial integro-differential equations, retarded integral inequalities, Wendroff's inequality