Show that the boundary conditions X(b)=wX(a) +zX'(a)

In summary, the conversation discusses boundary conditions and how to show that they are symmetric on the interval a<=x<=b if and only if the equation wd-zy=1 holds true. The concept of symmetry is explained as X(a) = X(b) and X'(a) = -X'(b). The person is seeking help in understanding what functions f(x) and g(x) need to be in order to solve the problem.
  • #1
matpo39
43
0
I need a little help getting started here,

Show that the boundry conditions X(b)=wX(a) +zX'(a)

and
X'(b) = yX(a) + dX'(a) on the interval a<=x<=b are symmetric if and only if wd-zy=1

i know that the a set of boundries are symmetric if f '(x)g(x) - f(x)g'(x) = 0 evaluated at x=a and x=b. but i am confused on what f(x) and g(x) would be.
if some one can help me get this problem started it would be greatly appreciated.

thanks
 
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  • #2
What would it mean for the BC to be 'symmetric'?

X(a) = X(b) and X'(a) = -X'(b) perhaps.
 

FAQ: Show that the boundary conditions X(b)=wX(a) +zX'(a)

What are boundary conditions?

Boundary conditions are the conditions that must be satisfied at the boundaries of a system or region in order for a mathematical model to accurately represent the physical situation. In other words, they define the behavior of a system at its boundaries.

Why is it important to consider boundary conditions in mathematical models?

Boundary conditions play a crucial role in determining the behavior and solutions of a mathematical model. They ensure that the model is realistic and applicable to the physical situation being studied. Without proper boundary conditions, a mathematical model may produce incorrect or meaningless results.

What does the equation X(b)=wX(a) +zX'(a) represent?

This equation represents a common form of boundary conditions known as the "Robin boundary condition." It is used to specify the relationship between the value of a function and its derivative at a boundary point. The coefficients w and z represent the weights given to the function value and derivative value, respectively.

How do you solve for X(x) in the equation X(b)=wX(a) +zX'(a)?

To solve for X(x), you would first need to determine the values of w and z. These coefficients can be found by considering the physical situation and the specific boundary conditions given. Once w and z are known, the equation can be solved using mathematical techniques such as separation of variables or numerical methods.

Can boundary conditions change in different situations?

Yes, boundary conditions can vary depending on the specific physical situation being studied. Different systems or regions may have different boundary conditions that need to be considered. It is important to carefully analyze and understand the physical situation in order to determine the appropriate boundary conditions to use in a mathematical model.

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