  Conservation laws are among the most fundamental geometric properties of a
partial differential equation (PDE), but few known finite difference methods
preserve more than one conservation law. All conservation laws belong to the
kernel of the Euler operator, an observation that was first used recently to
construct approximations symbolically that preserve two conservation laws of a
given PDE. However, the complexity of the symbolic computations has limited the
effectiveness of this approach. The current paper introduces some key
simplifications that make the symbolic-numeric approach feasible. To illustrate
the simplified approach, we derive bespoke finite difference schemes that
preserve two discrete conservation laws for the Korteweg-de Vries (KdV)
equation and for a nonlinear heat equation. Numerical tests show that these
schemes are robust and highly accurate compared to others in the literature.
