The Runge-Kutta methods are an important family of implicit and explicit iterative methods for the approximation of solutions of ordinary differential equations.
This is the first-order Runge-Kutta formula, which is the same as the Euler method.
This is the tenth-order Runge-Kutta formula.
This is the second-order Runge-Kutta formula, which can be implemented efficiently with a three-step algorithm.
This is the third-order Runge-Kutta formula.
This is the fourth-order Runge-Kutta formula.
This is the fifth-order Runge-Kutta formula.
This is the sixth-order Runge-Kutta formula.
This is the seventh-order Runge-Kutta formula.
This is the eighth-order Runge-Kutta formula.
The Runge-Kutta-Fehlberg method is a version of the classic Runge-Kutta method, which additionally uses step-size control and hence allows specification of a local truncation error bound.
This integrator works with a single-step stepper which estimates the solution for the next step given the solution of the current step.
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