Domain of Influence: PDEs Info

Thread starter gtfitzpatrick
Start date Feb 3, 2011
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In summary, the Domain of Influence in relation to Partial Differential Equations (PDEs) refers to the region where the solution is affected by initial or boundary conditions. It is determined by analyzing these conditions and can change during the course of solving a PDE problem. The accuracy of the PDE solution is heavily influenced by the Domain of Influence, and there are techniques that can be used to reduce its size and improve the accuracy of the solution.

Feb 3, 2011

gtfitzpatrick

Homework Statement

I don't have a real question, i was looking for where i could find info on the domain of influence, regarding pdes

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Feb 3, 2011

hunt_mat

Homework Helper

Most books on PDEs will have a section in it. For example the book, An introduction to partial differntial equations with MATLAB by Matthew Coleman

1. What is the meaning of Domain of Influence in relation to Partial Differential Equations (PDEs)?

Domain of Influence refers to the region in space or time where a solution to a PDE is affected by the initial or boundary conditions. It is the set of points where the solution is influenced by external factors and where the PDE is applicable.

2. How is the Domain of Influence determined for a given PDE problem?

The Domain of Influence is determined by analyzing the initial and boundary conditions of the PDE problem. These conditions define the boundaries of the solution region and identify the points where the solution is influenced by external factors.

3. Can the Domain of Influence change during the course of solving a PDE problem?

Yes, the Domain of Influence can change during the course of solving a PDE problem. This can occur if the initial or boundary conditions change or if the PDE itself is dependent on time or space variables.

4. How does the Domain of Influence affect the accuracy of a PDE solution?

The Domain of Influence plays a crucial role in determining the accuracy of a PDE solution. If the Domain of Influence is not properly defined, the solution may be inaccurate or even diverge. It is important to carefully analyze the Domain of Influence to ensure an accurate solution.

5. Are there any techniques to reduce the size of the Domain of Influence in PDE problems?

Yes, there are various techniques that can be used to reduce the size of the Domain of Influence in PDE problems. This can include changing the boundary conditions, using symmetry properties, or transforming the PDE into a different coordinate system. These techniques can help simplify the problem and improve the accuracy of the solution.