## Abstract

Entering now the vast field of partial differential equations, we immediately announce that our discussion shall be restricted to those types of equations that are of major importance in physics. These are the (“Quasilinear” means that the second derivatives of u appear in linear order only).

*quasilinear PDEs of second order*, which may be written in the general form$${a_{11}}\frac{{{\partial ^2}u}}{{\partial {x^2}}} + 2{a_{12}}\frac{{{\partial ^2}u}}{{\partial x\partial y}} + {a_{22}}\frac{{{\partial ^{2u}}}}{{a{y^2}}} + f\left( {x,y,u,\frac{{\partial u}}{{\partial x}},\frac{{\partial u}}{{\partial y}}} \right) = 0$$

(5.1)

## Keywords

Potential Equation Advective Equation Schroedinger Equation Cyclic Reduction Tridiagonal System
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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## Copyright information

© Springer Science+Business Media New York 1994