**Introduction**

This program gives coordinates for an
approximate solution for the differential
equation
using Euler's method.

If you have not used one of the programs posted on this website before,
you should read through
the information in the Intro to Programming
section first.

**The Program **

'EULERNUM' | {' is in ALPHA} {This is the name of the program} |

"INITIAL X"?X | {" is in ALPHA} {? is in PRGM} { is on the , button} |

"INITIAL Y"?Y | |

"STEP SIZE"?H | |

0C | {The 0 is a zero} |

Lbl 1 | {Lbl is in PRGM under JMP} |

C+1C | |

X+HU | |

Y+Y1 H V | {Y1 is in VAR under GPH, then followed by a 1} |

"STEP NUMBER" | |

C | { is in PRGM} |

"X COORD" | |

U | |

"Y COORD" | |

V | |

UX | |

VY | |

Goto 1 | {Goto is in PRGM under JMP} |

**Running the Program**

You will need to enter a function *f*(x,y) into
Y1 before
running the program. The program will ask for an
initial set of coordinates for X and Y and
a stepsize. The stepsize can be either positive or negative.
Hit EXE to see the X and Y coordinates of
each iteration.

*f*(x,y) = x + y,
Initial X = 1, Initial Y = 1,
Stepsize = 0.1

Your answer will be

X = 1.1, Y = 1.2

X = 1.2, Y = 1.43

X = 1.3, Y = 1.693

X = 1.4, Y = 1.9923

and so on