Numerical method of lines for first order partial differential-functional equations (Q1811432)

The authors discuss a method to solve the Cauchy problem for a nonlinear equation on the Haar pyramid, by using a discretization with respect to the spatial variables. The partial functional-differential equation is transformed into a system of ordinary functional-differential equations. The authors use differential-inequalities techniques to prove the convergence of the method of lines. Differential equations with retarded variables and differential-integral equations are particular cases of the general model considered in this paper. A numerical example is given to illustrate the theory.