  Many important initial value problems have the property that energy is
non-increasing in time. Energy stable methods, also referred to as strongly
stable methods, guarantee the same property discretely. We investigate
requirements for conditional energy stability of explicit Runge-Kutta methods
for nonlinear or non-autonomous problems. We provide both necessary and
sufficient conditions for energy stability over these classes of problems.
Examples of conditionally energy stable schemes are constructed and an example
is given in which unconditional energy stability is obtained with an explicit
scheme.
