What are boundary conditions differential equations
Next:Formulation methodsUp:Classification of partial differential equations (PDG) Previous:Example: characteristics procedure
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)
- 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
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