Numerical Analysis MATLAB Example - Backward Euler Method

How to use the Backward Euler method in MATLAB to approximate solutions to first order, ordinary differential equations. Demonstrates necessary MATLAB functions and coding practices for applying the Backward Euler method to real differential equations. fzero and optimset functions are demonstrated. For loops are used. Results are plotted against Forward Euler method, and dependence of solution accuracy on time step is demonstrated.

[@NinjadoPantanoPlays]

whoever you are you just saved my fucking live i love you

[@mohhamedsmith]

Awesome video. Thank you.

[@barschbubi]

How do you use this for a system of ode's? y'(Vector) = A (Matrix)*y(Vector)?

[@parthhalai7687]

How would I solve the Backward Euler Method (Implicit) if my function has both second-order derivative and first-order derivative?
For example:
m.(d^2y/dt^2) + c.(dy/dt) + k.y = F(t)
Where for the second order derivative I need to adopt a first order accurate scheme
(O(ℎ)) and for the first order derivative adopt a second order accurate scheme (i.e. O(ℎ^2))?

[@krishnabhogaonker3368]

You probably got an answer to this by now. But for the problem, you would just convert the second-order derivatives to first order. So you would have a first order system and then solve with implicit euler in the same way as normal.

[@mattiaguerini1458]

Great job 👍

[@engineeringmadeeasy4480]

Glad you found the video helpful, thanks!

[@lishengwang8583]

Thank you!

[@leon0163]

i have no idea what i did wrong but i keep getting this error
Unable to perform assignment because the indices on the left side are not compatible with the size of
the right side.

[@anikfaisal]

thanks for these lessons! where are the RK videos?

[@44urock]

what function is fzero in python?

[@Sinanmmd]

Hello dear sir, can you make a video on *NSFD (Nonstandard finite difference method)* ?

[@thatguyyouknow6586]

I love you