Vehicle–Track Coupled Dynamics by Wanming Zhai

Author:Wanming Zhai
Language: eng
Format: epub
ISBN: 9789813292833
Publisher: Springer Singapore

4.2.3 Accuracy of Zhai Method

Applying Taylor formula to , we have

(4.15)

where a supposed dot denotes a time derivative. Substituting Eq. (4.15) into Eq. (4.3) yields

(4.16)

Local truncation errors can then be written as

(4.17)

If ψ = 1/6 the order of accuracy of E(X) is O(Δt4), and if φ = 1/2 the order of accuracy of E(V) will be O(Δt3). Otherwise, the orders of accuracy decrease to O(Δt3) and O(Δt2), respectively. Obviously, the Zhai method has the same order of accuracy as that of the implicit Newmark-β method.

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