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Hi all, I'm writing myself a ordinary differential equation solver and I've already implemented several explicit integrators, which were pretty easy for me to do. Now I've decided to work on some implicit methods (for any stiff equations) and I've run into some issues.

The most basic one is the Backward Euler:

[tex]y_{n+1} = y_{n} + hf(t_{n+1}, y_{n+1})[/tex]

And as I understand, to solve this you need to use some iteration to get the value of [tex]y_{n+1}[/tex] to solve that equation for the next time step.

The problem I have is: How can I solve this? I thought I could use something like Newton's method, but I don't know how to properly apply it.

Any help, even a push in the right direction would be appreciated. Thanks!

The most basic one is the Backward Euler:

[tex]y_{n+1} = y_{n} + hf(t_{n+1}, y_{n+1})[/tex]

And as I understand, to solve this you need to use some iteration to get the value of [tex]y_{n+1}[/tex] to solve that equation for the next time step.

The problem I have is: How can I solve this? I thought I could use something like Newton's method, but I don't know how to properly apply it.

Any help, even a push in the right direction would be appreciated. Thanks!

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