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## Main Question or Discussion Point

I'm trying to write a code to implement he backwards Euler method to integrate the equation of motion. The sticking point seems to be that the acceleration is due to drag, and thus is dependent on the new position and velocity.

I understand the method to be:

[itex]v_{i+1}=v_{i}+a_{i+1}δ[/itex]

[itex]x_{i+1}=x_{i}+v_{i+1}δ[/itex]

With only the current conditions I can’t evaluate [itex]a_{i+1}[/itex] and am stuck.

Any help on how the implicit methods work would be really appreciated.

I’ve considered using [itex]a_{i+1}= a_{i}+ (a_{i}-a_{i-1}){δ} [/itex] but then that’s not really an implicit method is it? – you’re simply reusing the acceleration from last time around.

Thanks in advance,

I understand the method to be:

[itex]v_{i+1}=v_{i}+a_{i+1}δ[/itex]

[itex]x_{i+1}=x_{i}+v_{i+1}δ[/itex]

With only the current conditions I can’t evaluate [itex]a_{i+1}[/itex] and am stuck.

Any help on how the implicit methods work would be really appreciated.

I’ve considered using [itex]a_{i+1}= a_{i}+ (a_{i}-a_{i-1}){δ} [/itex] but then that’s not really an implicit method is it? – you’re simply reusing the acceleration from last time around.

Thanks in advance,