Thus far we've taken the step size h to be positive, and therefore we've developed solutions to the right of the initial point. Is Euler's method valid if we use a negative step size h &lt; 0 and develop a solution to the left?I think it is not possible.How we can explain that it is possible or not?

Question

Thus far we&#039;ve taken the step size   h to be positive, and therefore we&#039;ve developed solutions to the right of the initial point. Is Euler&#039;s method valid if we use a negative step size   h  &amp;lt;  0 and develop a solution to the left?I think it is not possible.How we can explain that it is possible or not?

Jamal Hamilton · Accepted Answer

Yes, the process of computation stays the same when   h  &amp;lt;  0; you get a solution to the left of the initial point. An adjustment in error bound formulas may be needed, since they are written under the assumption   h  &amp;gt;  0. So, replace   error  ≤  C  h with   error  ≤  C      |    h      |  .Using   h  &amp;lt;  0 in Euler&#039;s method is different from using Backward (aka implicit) Euler method.

Thus far we've taken the step size h to be positive, and therefore we've developed solutions t

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