- #1
Numerical Analysis Euler's Method
- Thread starter mayaitagaki
- Start date
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Homework Help Overview
The discussion revolves around applying Euler's Method to a system of differential equations involving both dy/dx and dz/dx. The original poster, Maya, presents initial conditions and a specified step size for the calculations.
Discussion Character
- Exploratory, Mathematical reasoning
Approaches and Questions Raised
- Maya expresses confusion regarding the inclusion of two variables in the differential equations and seeks clarification. Other participants suggest performing Euler calculations using the provided equations and initial values.
Discussion Status
Some participants have provided guidance on how to approach the calculations, specifically by suggesting the use of the initial values to compute the derivatives. There appears to be a productive exchange, with Maya indicating she has gained understanding from the responses.
Contextual Notes
The problem involves specific initial conditions and a defined range for x, which may influence the calculations. Maya's initial uncertainty highlights the complexity of handling multiple variables in differential equations.
- #2
vela
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What don't you get?
- #3
HallsofIvy
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Just do two Euler calculations.
Since the d.e. are
\frac{dy}{dx}= -2y+ 4e^{-x}
and
\frac{dz}{dx}= -\frac{yz^2}{3}
use the given initial values x= 0, y= 2, and z= 4 to calculate the two right sides:
\frac{dy}{dx}= -2(2)+ 4e^{0}= -4+ 4= 0
and
\frac{dz}{dx} -\frac{(2)(16){3}= \frac{32/3}= -10.66666...<br /> <br /> Since h= .2, x= 0+ h= 0+ .2= .2, y= 2+ (dy/dx)h= 2 - 0= 2, z= 4+ (dz/dx)h= 4- 2.133333= 1.8666668. <br /> <br /> and repeat.
Since the d.e. are
\frac{dy}{dx}= -2y+ 4e^{-x}
and
\frac{dz}{dx}= -\frac{yz^2}{3}
use the given initial values x= 0, y= 2, and z= 4 to calculate the two right sides:
\frac{dy}{dx}= -2(2)+ 4e^{0}= -4+ 4= 0
and
\frac{dz}{dx} -\frac{(2)(16){3}= \frac{32/3}= -10.66666...<br /> <br /> Since h= .2, x= 0+ h= 0+ .2= .2, y= 2+ (dy/dx)h= 2 - 0= 2, z= 4+ (dz/dx)h= 4- 2.133333= 1.8666668. <br /> <br /> and repeat.
- #4
mayaitagaki
- 8
- 0
thanks sooooo much! I've got it!
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