Characteristic Lines for 2D Equations with a Boundary Condition

In summary, to find the characteristic lines for the equation 2 du/dx + 8x du/dt = 16x, we can use the formula dt/dx = b/a, where a = 2 and b = 8x. This gives us dt/dx = 4x. From here, we can solve for t by integrating both sides. The result is t = 2x^2 + C, where C is a constant. We can then use the boundary condition u(x,0) = x^2 to solve for C, giving us a final characteristic of t = 2x^2 + t1 - 2x^12. However, this answer may not be correct as it
  • #1
andrey21
476
0
Find the characteristic lines for the equation:

2 du/dx + 8x du/dt = 16x




Here's my attempt

a = 2 b = 8x c = 16x

Using dt/dx = b/a = 8x/2 = 4x

t = 2x2 + C

C = t1 -2x12

Hence the characteristic is:

t = 2x2 + t1 - 2x12
 
Physics news on Phys.org
  • #2
Please any reply would be great, am I correct with my answer??
 
  • #3
1. You can't expect people to anwer within two hours. People don't just sit around waiting for a new post!

2. You can get yourself an infraction and even banned for "bumping" threads just to get them moved to the top of the list again.

3. I don't even understand your answer. The characteristic is a relation between x and y. There is no "y" in your answer but there is a "t" which shouldn't be there.
 
  • #4
All of the examples I have been given they do not contain a "y", I should have stated the boundary condition is u(x,0) = x^(2).
 

FAQ: Characteristic Lines for 2D Equations with a Boundary Condition

What is the concept of characteristic lines?

The concept of characteristic lines refers to a mathematical method used to solve partial differential equations. It involves finding solutions along specific lines in a given domain, known as characteristic curves, which have a constant slope in relation to the equation being solved.

How is the method of characteristic lines used in scientific research?

The method of characteristic lines is commonly used in various fields of science, such as physics, engineering, and geology. It allows for the efficient and accurate solution of complex partial differential equations, which are often encountered in these fields.

What are the advantages of using the method of characteristic lines?

The method of characteristic lines has several advantages, including its ability to solve nonlinear equations, its ability to handle multiple dimensions, and its efficient use of computational resources. It also provides insight into the behavior of solutions along specific lines in the domain.

What are some limitations of the method of characteristic lines?

One limitation of the method of characteristic lines is that it may not always provide a unique solution, especially in cases where the initial conditions or boundary conditions are not well-defined. It also requires a good understanding of the underlying equations and their characteristics.

What are some real-world applications of the method of characteristic lines?

The method of characteristic lines has many real-world applications, such as in the design of aircraft wings, the prediction of weather patterns, and the simulation of fluid flow in pipes and channels. It is also widely used in the development of computer models for various scientific and engineering problems.

Similar threads

Verify Green's Theorem in the given problem
Replies
10
Views
1K
Solve the given second order differential equation
Replies
14
Views
877
Find the value of the definite integral
Replies
8
Views
1K
Solve the problem that involves iteration
Replies
21
Views
1K
Equations of Parallel Tangent Lines to f(x)=3x(5x^2+1)
Replies
11
Views
2K
Differentiation of a Quotient check
Replies
3
Views
1K
Is the Calculation of the Vector Line Integral Over a Square Correct?
Replies
12
Views
2K
Differentiate the given integral
Replies
15
Views
1K
Have I got this correct? (Quotient rule)
Replies
2
Views
1K
How Do You Correctly Apply the Product and Quotient Rules in Differentiation?
Replies
1
Views
1K

Hot Threads

Recent Insights

Back
Top