The Lax-Wendroff second-order scheme follows from a Taylor series retaining the three terms:

.

The first temporal derivative in the above equations is directly replaced using the differential equation. But the second-derivative term is examined in more detail. Considering the original equation and taking its time derivative in the form:

, ,

__where__

Making __the
substitution__ yields

.

Using central differencing for derivatives, the Lax-Wendroff second-order numerical scheme is obtained:

.

Making the substitution yields

.

Using central differencing for derivatives, the Lax-Wendroff second-order numerical scheme is obtained:

.

The Jacobian matrix is computed at the half interval as

In Burgers’ equation, and , therefore