Numerical Analysis - Backward Euler Method

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Simple derivation of the Backward Euler method for numerically approximating the solution of a first-order ordinary differential equation (ODE). Builds upon knowledge presented in lesson on the Forward Euler method. Comparison between the Forward Euler and Backward Euler methods is presented, as it pertains to solving first order ordinary differential equations.
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I'm utilizing this for my summer research and was looking for a clear and concise explanation, very well done! Thank you so much!

deborahfranza
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Please solve any question using this method, through which we clearly understand.

gulshankarim
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How do you plug y_n+1 into the equation if it's the thing you're looking for????

MH-ixnh
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Thank you very much for the clear explanation. Now I can do my tutorial sheet!

May I ask what '0(deltat^2)' represents when describing the local error?

Thanks!

JoshuaNg-ox
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Very short yet very clear explanation. Thank you very much.

yizhang
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If I'm updating position, y, based on a force of gravity, G m1 m2 G/ r^2, how do solve for y n+1? (Trying to put this in code for a gravity simulation)

TheRainHarvester
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Thank you much.
Best explanation on the yt!!

icee
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Thank you for the video, it was very helpful.

ceroorec
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How do you choose stopping criterion if you use euler method in while loop?

rhot
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how to implement this for nth order system of ODE?

anishadevi