Euler's Method: Derivation

Learn how to derive Euler's method of solving a first order ordinary differential equation.
http://numericalmethods.eng.usf.edu

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Education

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• Euler's
• Method:
• Derivation
• ordinary
• differential
• equations
• numerical
• methods
• numericalmethodsguy

[o0MetalSnake0o]

dy/dx=x^2*y ; y(0)=1; find y(.6)...this is he problem that i am stuck on, i cant seem to get an approximate value that is close to the Actual value(1.075)

[numericalmethodsguy]

@o0MetalSnake0o First you need to choose a step size. Let's keep it simple as h=0.2. In this case, the intermediate approximate values are y1=1, y2=1.008 and y3=1.04026 at x=0.2, 0.4 and 0.6, respectively. The last value is the approx value of y(0.6) which is within 3.2% of the exact value of 1.07466. Choose a smaller h for better accuracy. 

[o0MetalSnake0o]

so would y(1)=y sub 1

[numericalmethodsguy]

@o0MetalSnake0o y sub 1 is y (x1), not y(1). If you are calculating y sub i, the value of y is being calculated at (x sub 0)+i*h.

[blkscreen15]

thanks for explaining f(x,y) and sometime when you are confused about the smallest thing, its hard to understand other stuff, so this is great and very helpful video.

[ctw005]

amazing teacher

[kanishkagoel17]

Sir, do you have Backwards Euler Method Explained anywhere in your videos? Also thank you for all your videos so far. They have been very helpful.

[harishli2020]

very good explanation.....



[saionjik]

Thanks, I learned this the second time from you. Rasvan didn't spend too much time on this method in beginning DE. :) Interesting topic. Sadly the semester is almost over and I'm no longer motivated to do work in the class because my grade is too good.

[imvolkan]

excellent explanation, simple and plain. Very informative video! Thank you

[urbandiscipline88]

excellent explaination!