Unformatted text preview: x ( t i ), the diﬀerence, assuming no rounding is introduced, is | x i-x ( t i ) | , and is called the local truncation error . The following theorem shows how the local truncation error is depending on f ( t,x ) and h , Theorem 2.1 . Suppose f ( t,x ) , ∂f ( t,x ) ∂t , and ∂f ( t,x ) ∂x are continuous on [a, b], and h = b-1 n is the step size. Furthermore let x ( t ) be the solution of initial value problem x = f ( t,x ) ,x ( a ) = x and x i = x i-1 + f ( t i-1 ,x i-1 ) * h be the approximate of x ( t i ) , and let e i = x ( t i )-x i be...
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- Spring '11
- Numerical Analysis, local truncation error