I don't quite understand the discretisation error of Euler's method L ( t , h...

glutynowy44

glutynowy44

Answered

2022-07-07

I don't quite understand the discretisation error of Euler's method
L ( t , h ) = x ( t + h ) x ( t ) h f ( t , x ( t ) )
What I don't understand is: x ( t + h ) x ( t ) h is the "gradient" and f ( t , x ( t ) is the value of the function. How can we get the error by subtracting the former by the latter?

Answer & Explanation

Caiden Barrett

Caiden Barrett

Expert

2022-07-08Added 20 answers

You assume that x ( t ) is an exact solution to x ˙ = f ( t , x ) and then apply Taylor formulas.

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