A NOTE ON EXPLICIT THREE-DERIVATIVE RUNGE-KUTTA METHODS (ThDRK)
نویسندگان
چکیده
Recently, the Runge-Kutta methods, obtained via Taylor’s expansion is exist in the literature. In this study, we have derived explicit methods for problems of the form y′ = f(y) including second and third derivatives , by considering available Two-Derivative Runge-Kutta methods (TDRK). The methods use one evaluation of first derivative, one evaluation of second derivative and many evaluations of third derivative per step. The methods can be named as ThreeDerivative Runge-Kutta methods, ThDRK shortly. We present methods with stages up to three and order up to seven. Comparisons is made with other some existing methods on some standard problems. The stability region of the methods are given.
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