Geodesic
A three-dimensional family of seven-step Runge-Kutta methods of order six
Numerical methods and programming, Tome 2 (2001) no. 1, pp. 159-166

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A new family of seven-step Runge-Kutta methods of order six is found. An analytical technique for deriving formulas of this type is proposed. A numerical example is given. It is shown that the analytically determined coefficients of our method coincide to a high accuracy with those computed approximately with the Newton-Raphson procedure.
Keywords: ordinary differential equations, Runge-Kutta methods, Newton's method for nonlinear equations, numerical methods. 
@article{VMP_2001_2_1_a10,
     author = {G. M. Khammud},
     title = {A three-dimensional family of seven-step {Runge-Kutta} methods of order six},
     journal = {Numerical methods and programming},
     pages = {159--166},
     publisher = {mathdoc},
     volume = {2},
     number = {1},
     year = {2001},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMP_2001_2_1_a10/}
}
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G. M. Khammud. A three-dimensional family of seven-step Runge-Kutta methods of order six. Numerical methods and programming, Tome 2 (2001) no. 1, pp. 159-166. http://geodesic.mathdoc.fr/item/VMP_2001_2_1_a10/