Initial Value Problems for Linear Shooting Method

In summary, the conversation is discussing how to derive and submit initial value problems for u(x) and v(x) from the equation y''-by'=f(x). The speaker is unsure of what is being asked and how u(x), v(x), and f(x) are related. Another speaker mentions that u+av is a linear combination of y, with initial conditions u'(0)=0 and v'(0)=1.
  • #1
danbone87
28
0

Homework Statement



y''-by'=f(x)

I have to "derive and submit the appropriate initial value problems (with initial conditions) for u(x) and v(x). Show me all 4 equations and initial conditions... "

and I know you get u(x) and v(x) by solving ivp's for the original equation, one homogeneous and one not. but do i use two initial guesses for y'(0)=? and then i have 4 of those? I'm unsure of what is being asked exactly.
 
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  • #2
danbone87 said:
y''-by'=f(x)

i'm unsure of what is being asked exactly.

So am I. What is f(x), u(x) and v(x) and how are they related?
 
  • #3
u+av

is a linear combination of y. such that u'(0) = 0 and v'(0)=a
 
  • #4
whoops, v'(0)=1
 

What is the Linear Shooting Method?

The Linear Shooting Method is a numerical method used to approximate solutions to ordinary differential equations (ODEs). It involves transforming a higher-order ODE into a system of first-order ODEs and solving them using an initial value problem solver.

What types of problems can be solved using the Linear Shooting Method?

The Linear Shooting Method can be used to solve initial value problems for ordinary differential equations, including boundary value problems and two-point boundary value problems.

What is the difference between the Linear Shooting Method and the Finite Difference Method?

The Linear Shooting Method approximates the solution to a differential equation by solving a system of first-order ODEs, while the Finite Difference Method approximates the solution by discretizing the domain and solving a system of algebraic equations.

What are the advantages of using the Linear Shooting Method?

The Linear Shooting Method is a versatile and accurate method for solving a wide range of ODEs. It can handle discontinuous or singular solutions and is relatively easy to implement. It also allows for the computation of higher-order derivatives of the solution.

What are the limitations of the Linear Shooting Method?

The Linear Shooting Method can be computationally expensive for large systems of ODEs. It may also be unstable for certain types of ODEs, particularly those with solutions that grow rapidly. Additionally, it may not be suitable for highly nonlinear or stiff problems.

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