The Runge Kutta method solves ordinary differential equations with initial conditions. The Runge Kutta method works with a fixed step rate but with a higher degree of accuracy than the common Euler method. Details
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X is an array of strings of variables. |
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time start is the start point of the ODE. The default is 0. |
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time end is the end point of the time interval under investigation. The default is 1.0. |
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h is the fixed step rate. The default is 0.1. |
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X0 is the vector of the start condition
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time is the string denoting the time variable. The default variable is t. |
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F(X,t) is a 1D array of strings representing the right sides of the differential equations. |
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Times is an array representing the time steps. The Runge Kutta method yields equidistant time steps between time start and time end. |
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X Values is a 2D array of the solution vector
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ticks is the time in milliseconds for the whole calculation. |
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errors are produced by using the wrong inputs X, X0, and F(X,t). |
The Runge Kutta method of 4th order works as a five stage process, more precisely
The method ends if
The illustration below shows the solution of the following system of ordinary differential equations:
Enter the following equations on the front panel:
![]() | Note Even though there are actually three solutions, a first glance at the graph almost seems to show only two solutions. This is because the solutions for x and y are very similar, so they almost overlap. |