In the work of [12], explicit Runge-Kutta schemes of stages up to four with the first derivative were constructed. Following the work [12], a family of Runge-Kutta type method with higher order ...

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19. fieldlines3D（fieldlines3D(X,Y,Z,U,V,W,x0,y0,z0) plots a field line with the initial point P(x0,y0,z0).The matrices X,Y,Z,U,V,and W must all be the same size and contain corresponding position and field components.The function employs the 4th order Runge-Kutta method for solving numerically differential equation y'=f(x,y).）

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May 19, 2017 · The aim of this research is to study the efficiency of symplectic and non-symplectic Runge-Kutta methods in solving Kepler problem. The numerical behavior of the Runge-Kutta (RK) methods that are symmetric such as the implicit midpoint rule (IMR), implicit trapezoidal rule (ITR), 2-stage and 2-stage Gauss (G2) method are compared with the non-symmetric Runge-Kutta methods such as the explicit ...

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It is known that implicit SSP Runge-Kutta methods exist only up to sixth order; however, if we restrict ourselves to solving only linear autonomous problems, the order conditions simplify and we can find implicit SSP Runge-Kutta methods of any linear order.

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Runge Kutta (RK) C++ Program. Python Programming. Ordinary Differential Equation Using Fourth Order Runge Kutta (RK) Method Pseudocode.