i have this differential equation and actually i am not sure if i have solved it right with Euler's improved method : z ″ = f z − C z ∗ | z ′ | ∗ z ′ z ′ = u u ′ = z ″ = f z − C z ∗ | u | ∗ uImproved Euler Method : K 1 = f z − C z ∗ | u n | ∗ u n K 2 = f z − ( C z ∗ | u n + h ∗ K 1 | ) ∗ ( u n + h ∗ K 1 )so we get : z n + 1 = z n + h ∗ u n u n + 1 = u n + h 2 ∗ ( K 1 + h ∗ K 2 )Is this right ?P.S (fz , Cz are just variables with numbers not function inputs)

Question

i have this differential equation and actually i am not sure if i have solved it right with Euler&#039;s improved method :      z    ″    =      f          z        −      C          z        ∗      |        z    ′        |    ∗      z    ′        z    ′    =  u      u    ′    =      z    ″    =      f          z        −      C          z        ∗      |    u      |    ∗  uImproved Euler Method :      K          1        =  f      z    −  C      z    ∗      |        u          n            |    ∗      u          n            K          2        =  f      z    −  (      C          z        ∗      |        u          n        +  h  ∗      K          1            |    )  ∗  (      u          n        +  h  ∗      K          1        )so we get :      z          n      +      1        =  z      n    +  h  ∗      u          n            u          n      +      1        =      u          n        +      h    2    ∗  (      K          1        +  h  ∗      K          2        )Is this right ?P.S (fz , Cz are just variables with numbers not function inputs)

Trace House · Accepted Answer

There are several small errors that would sum up to a more grossly incorrect output. As a system with multiple components, you need to compute the intermediary slopes at all stages for all components, that is, additionally for the slopes in   z direction                              L          1                                    =        u                                      L          2                                    =        u        +        h                  K          1                    Then the equations for the step are                              u                      +            1                                              =        u        +                  h          2                (                  K          1                +                  K          2                )                                      z                      +            1                                              =        z        +                  h          2                (                  L          1                +                  L          2                )        =        z        +        h        u        +                              h            2                    2                          K          1

Bruno Thompson · Accepted Answer

Thanks alot for the comprehensive response