**Systems of ODEs: Third order Heun**

This app uses **third order Heun** IVP method to numerically approximate the solution of a system of ordinary differential equations

\(\qquad \dfrac{\mathrm{d} x_{1}}{\mathrm{d} t} = f_{1}'(t, y) \)

\(\qquad \dfrac{\mathrm{d} x_{2}}{\mathrm{d} t} = f_{2}'(t, y) \)

\(\qquad\qquad \vdots\)

\(\qquad \dfrac{\mathrm{d} x_{n}}{\mathrm{d} t} = f_{n}'(t, y) \)

with \( a \leq t \leq b, \quad x_{1}(a) = \alpha_{1}, x_{2}(a) = \alpha_{2}, \cdots, x_{n}(a) = \alpha_{n}.\)

and plots the results on a graph for visualization purposes.

Label | Description / Your input | |
---|---|---|

1 | A system of \(n\) ODE equations. | |

2 | Start and end time points respectively. | |

3 | Value of dependent variable at time zero, \(y_{0} = y(t_{0})\). | |

4 | Either the number of steps, \(n\) specified as an integer or the step-size, \(h\) where \(t_{0} < h < t_{f}\). | |

5 | Initial value problem method to be used to solve the systems ODE equations numerically. | |

6 | Number of iterations to display. | |

7 | Decimal points to display (does not affect internal precision). | |

**Systems of ODEs: Third order Heun**

Enter your valid inputs then click

**Systems of ODEs: Third order Heun**

Enter your valid inputs then click

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