Maintaining Solution Invariants in the Numerical Solution of ODE s

Techniques for maintaining the numerical consistency of equality and inequality invariants known to be obeyed by the true solutions of ODES are discussed. Shampine [11] has examined the problem and made some recommendations for one-step methods. A general framework is used to justify a.particular form of his technique for both one-step and multistep methods in the case of equality invariants. This framework can also be used for inequality invariants, but is not satisfactory for multistep methods. However, in a large class of inequality invariants, typified by those arising in chemical kinetic problems, it is shown that the invariant can be satisfied automatically by the numerical method.