What are boundary conditions differential equations


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Initial and boundary conditions

 

When integrating partial equivalents, functions arise (similar to the integration constants for ordinary equivalents). A closed solution is only obtained if it can be determined by additional conditions. A distinction is made between initial and boundary conditions.

Initial conditions
are rules for the value of the dependent variable in the initial state.

boundary conditions
are rules for the value of the dependent variable or its derivation on the range boundary.

The following boundary conditions are known by name:

    1. Dirichlet binding:
    The value of the appended variable is given along the edge of the area.
    2. Neumann binding:
    The normal derivative of the independent variable along the edge is given.
    3.Mixed (Cauchy)
    Boundary conditions:
    Dirichle boundary conditions are given on one part of the boundary, Neumann conditions on another.
    4. Robin condition:
    This means linear combinations of Dirichlet and Neumann conditions.

Danger: Pure gradient conditions can solve the problem Not solve clearly, as the level is not fixed.



Next:Formulation methodsUp:Classification of partial differential equations (PDG) Previous:Example: characteristics procedureBenjamin Guild
Sat Dec 16 3:24:45 pm CET 2000