Feagin, Terry2020-04-272020-04-272012-12Feagin, T., “High-order Explicit Runge-Kutta Methods Using M-Symmetry,” Neural, Parallel & Scientific Computations, Vol. 20, No. 4, December 2012, pp. 437-458https://hdl.handle.net/10657.1/2296The Runge-Kutta equations of condition are reformulated. The concept of m-symmetry is defined. It is shown that any m-symmetric method is of order m. The equations of condition for a twelfth-order explicit Runge-Kutta method with twenty-five stages are solved using m-symmetry. The method contains an embedded tenth-order method that can be used to estimate the local truncation errors and thus to vary the stepsize. Numerical experiments demonstrate that the method compares favorably with other high-order methods, especially for those problems requiring highly accurate solutions.en-USArticle