A method for approximate solution in \(C^2\) of a hyperbolic equation with Lipschitz nonlinearity (Q1395328)

The author considers a problem on a half-line for a hyperbolic partial differential equation with nonhomogeneous boundary conditions. The right-hand side of the equation depends on the solution and satisfies the Lipschitz condition. An algorithm is suggested that delivers a solution and its partial derivatives up to the second order in the characteristic triangle. The method is constructed by reducing the original problem to an equivalent system of integral equations.