THE USE OF HAMILTONS PRINCIPLE TO DERIVE TIME-ADVANCE ALGORITHMS FOR ORDINARY DIFFERENTIAL-EQUATIONS

Hamilton's principle is applied to derive a class of numerical algorit hms for systems of ordinary differential equations when the equations are derivable from a Lagrangian. This is an important extension into t he time domain of an earlier use of Hamilton's principle to derive alg orithms for the spatial operators in Maxwell's equations. In that work , given a set of expansion functions for spatial dependences, the Vlas ov-Maxwell equations were replaced by a system of ordinary differentia l equations in time, but the question of solving the ordinary differen tial equations was not addressed. Advantageous properties of the new t ime-advance algorithms have been identified analytically and by numeri cal comparison with other methods, such as Runge-Kutta and symplectic algorithms. This approach to time advance can be extended to include p artial differential equations and the Vlasov-Maxwell equations. An int eresting issue that could be studied is whether a collisionless plasma simulation completely based on Hamilton's principle can be used to ob tain a convergent computation of average properties, such as the elect ric energy, even when the underlying particle motion is characterized by sensitive dependence on initial conditions.