Initial Value Problems for Linear Shooting Method

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Homework Help Overview

The discussion revolves around the formulation of initial value problems related to the linear shooting method for the differential equation y'' - by' = f(x). Participants are tasked with deriving appropriate initial conditions for functions u(x) and v(x) and clarifying their relationships.

Discussion Character

  • Exploratory, Conceptual clarification, Problem interpretation

Approaches and Questions Raised

  • Participants express uncertainty about the requirements for deriving initial value problems, specifically regarding the definitions and roles of u(x), v(x), and f(x). There is discussion about the initial conditions needed for the functions and the relationship between them.

Discussion Status

The discussion is ongoing, with participants seeking clarification on the problem statement and the relationships between the variables involved. Some guidance has been offered regarding the initial conditions, but there is no consensus on the overall approach yet.

Contextual Notes

Participants are grappling with the definitions of the functions involved and the specific initial conditions required for the problem, indicating a need for further exploration of the problem setup.

danbone87
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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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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?
 
u+av

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

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