Splitting schemes for solution

5.3 Increase of the accuracy of time deriva- tives approximation using the Lax-Wendroff scheme

Let us consider the general transport equation:

@u

@F .u/

C D 0 (5.24)

@t

@x

We introduce the following designations:

@F

AD @u

u tt D F xt D F tx ; F t D F u u t D F u F x

AF x

Substitution of these results into the time Taylor series gives the Lax-Wendroff scheme which is of the second order in time:

D u.t/ 3

x .t / C .A.t /F x .t // x

A difficulty arising in the LW approach is the computation of the operator A. One can easy derive that the Lax Wendroff scheme results in the solution of the equation:

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