COMPLETE SOLUTION OF FIFTH ORDER RUNGE-KUTTA EQUATIONS

A fifth order Runge-Kutta integration formula applicable to systems of first order differential equations involves 21 parameters which must satisfy 17 equations. Article shows the equations in a condensed matrix form, introduces a set of coefficients of a linear dependence, divides the solutions into cases, and specifies all conditions which the parameters are required to satisfy to assure the existence of solutions. The derivations leading to the solutions given assumed the solutions to be nonsingular, but some, at least, of the singular solutions are obtainable as limiting cases, with fairly obvious modifications, of the nonsingular solutions.