Abstract
The method of lines for partial differential equations consists in replacing spatial derivatives by difference expressions. Then the partial equation is transformed into a system of ordinary differential equations. The method is used for approximation of solutions of nonlinear differential problems of parabolic type by solutions of ordinary equations ([91, 153, 219, 220, 222, 225, 238]). The method is also treated as a tool for proving of existence theorems for differential problems corresponding to parabolic equations [223, 224, 227] or first-order hyperbolic systems [101, 157]. Simple examples of the method of lines for nonlinear functional differential equations were considered in [29, 108, 128]. The method for equations of higher orders is studied in [91]. The book [189] demonstrates lots of examples of the use of the numerical method of lines. Convergence analysis of one step difference methods generated by the numerical method of lines was investigated in [186].
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