Numerical methods for ordinary differential systems: the initial value problem
Numerical methods for ordinary differential systems: the initial value problem
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Solutions of third-order differential equations relevant to draining and coating flows
SIAM Journal on Mathematical Analysis
A history of Runge-Kutta methods
Applied Numerical Mathematics - Special issue on selected keynote papers presented at 14th IMACS World Congress, Atlanta, NJ, July 1994
Runge-Kutta methods: some historical notes
Applied Numerical Mathematics - Special issue celebrating the centenary of Runge-Kutta methods
Thin Films with High Surface Tension
SIAM Review
Numerical methods for ordinary differential equations in the 20th century
Journal of Computational and Applied Mathematics - Special issue on numerical anaylsis 2000 Vol. VI: Ordinary differential equations and integral equations
Numerical Initial Value Problems in Ordinary Differential Equations
Numerical Initial Value Problems in Ordinary Differential Equations
International Journal of Computer Mathematics
A direct variable step block multistep method for solving general third-order ODEs
Numerical Algorithms
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This paper is devoted to the investigation of direct integrators of Runge-Kutta type for third-order ordinary differential equations (RKT). A new tri-colored tree theory and the corresponding B-series theory are built systematically, based on which the order conditions for RKT methods are derived. A two-stage explicit RKT method of order four and a three-stage explicit RKT method of order five are constructed. Implicit RKT methods of collocation type are considered. The results of numerical experiments show that our explicit RKT methods are more efficient than the traditional RK methods of the same algebraic order.