i have this differential equation and actually i am not sure if i have solved...

Makena Preston

Makena Preston

Answered

2022-07-19

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 | u
Improved 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)

Answer & Explanation

Trace House

Trace House

Expert

2022-07-20Added 7 answers

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

Bruno Thompson

Expert

2022-07-21Added 9 answers

Thanks alot for the comprehensive response

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