Simple Euler and Implicit Euler

You're correct. And, can replace the "Euler" in your statement with "method," e.g., your statement is true of all explicit methods vs. all implicit methods. Implicit methods solve the entire interdependent system simultaneously for each integration step, and local changes affect the entire portion of the domain that they should affect in that one step. Explicit methods, such as explicit Euler, affect only local neighborhood in each integration step so it might take several steps for a local change to propogate throughout the domain. Errors and instabilities can creep in when you have to propogate changes over several steps..does this help?

There are complications...when dealing with hyperbolic and parabolic PDE's vs. elliptic PDE's...but that's for another discussion.

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Original post by grhodes_at_work You're correct. And, can replace the "Euler" in your statement with "method," e.g., your statement is true of all explicit methods vs. all implicit methods. Implicit methods solve the entire interdependent system simultaneously for each integration step, and local changes affect the entire portion of the domain that they should affect in that one step. Explicit methods, such as explicit Euler, affect only local neighborhood in each integration step so it might take several steps for a local change to propogate throughout the domain. Errors and instabilities can creep in when you have to propogate changes over several steps..does this help? There are complications...when dealing with hyperbolic and parabolic PDE's vs. elliptic PDE's...but that's for another discussion.

Thanks for the fast reply. It helps a lot. That was actually my initial confusion a few months back when I was developing a system using the mass spring model with an explicit method. I was confused because it seems like by restoring one spring might invalidate another spring which was earlier restored in the same time-step.

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Original post by Mystery I was confused because it seems like by restoring one spring might invalidate another spring which was earlier restored in the same time-step.

Yep!