Characterstic Curves and domain of dependence

Thread starter Nik23S
Start date Apr 10, 2010
Tags

Curves Domain

In summary, characteristic curves are a set of mathematical curves used to describe the evolution of a solution in partial differential equations. They are related to the domain of dependence, which is the region of space and time that influences the behavior of the solution. Understanding these concepts is crucial in solving equations and predicting the behavior of physical systems. They can also be applied to real-world problems in various fields of science and engineering. While characteristic curves are a mathematical concept, the domain of dependence is a physical concept derived from them.

Apr 10, 2010

Nik23S

Please give geometrical desciption of what are characterstic curves and domain of dependence of a PDE. Please help.
Thanks.

Physics news on Phys.org

Apr 10, 2010

IttyBittyBit

What part of it don't you understand? I'm just saying you will get many more replies if you ask specific questions instead of really general ones.

1. What are characteristic curves?

Characteristic curves are a mathematical concept used in the study of partial differential equations. They are a set of curves that describe the evolution of a solution at a given point in space and time.

2. How are characteristic curves related to the domain of dependence?

The domain of dependence is the region of space and time that influences the behavior of a solution at a given point. Characteristic curves determine the shape of this region and are used to analyze the behavior of the solution within it.

3. What is the importance of understanding characteristic curves and the domain of dependence?

Understanding characteristic curves and the domain of dependence is crucial in solving partial differential equations and predicting the behavior of physical systems. It allows us to determine the stability and accuracy of numerical methods used to approximate solutions.

4. Can characteristic curves and the domain of dependence be applied to real-world problems?

Yes, characteristic curves and the domain of dependence are used extensively in various fields of science and engineering, such as fluid dynamics, electromagnetics, and quantum mechanics. They provide a powerful tool for understanding and predicting the behavior of complex systems.

5. How do characteristic curves and the domain of dependence differ from each other?

While characteristic curves are a set of curves that describe the evolution of a solution at a given point, the domain of dependence is a region of space and time that influences the behavior of a solution at that point. In other words, characteristic curves are a mathematical concept, while the domain of dependence is a physical concept derived from them.