Partial Differential Equations

  • Franz J. Vesely
Chapter

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 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)
(“Quasilinear” means that the second derivatives of u appear in linear order only).

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

Authors and Affiliations

  • Franz J. Vesely
    • 1
  1. 1.Institute of Experimental PhysicsUniversity of ViennaViennaAustria

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