Laboratorio Metodos Numericos

Introduccion

Ecuaciones diferecnciales
Resuelva los siguientes problemas de cauchy mediante los métodos de Euler, Euler Mejorado y Runge-kutta.

EULER
y'=x+y, y0=1, y1=?

X | y |yn+1=yn+h(f(xn, yn)) |
0 | 1 | -------------- |
0.1 | 1.1 | 1+0.1(0+1) |
0.2 | 1.22 | 1.1+0.1(0.1+1.1) |
0.3 | 1.362 | 1.22+0.1(0.2+1.22) |
0.4 | 1.5282 | 1.362+0.1(0.3+1.362) |
0.5 |1.72102 | 1.5282 +.01(0.4+1.5282) |
0.6 | 1.943122 | 1.72102+0.1(0.5+1.72102) |
0.7 | 2.1974342 | 1.943122+0.1(0.6+1.943122) |
0.8 | 2.48717762 | 2.1974342+0.1(0.7+2.1974342) |
0.9 | 2.81585382 |2.48717762+0.1(0.8+2.48717762) |
1.0 | 3.18748492 | 2.81585382+0.1(0.9+2.81585382) |

y'=2yx2+1x2, y1=0, y1.5=?
X | y | yn+1=yn+h(f(xn, yn)) |
1 | 0 | |
1.1 | 0.1 | |
1.2 | 0.1983| |
1.3 | 0.2893 | |
1.4 | 0.3636 | |
1.5 | 0.4085 | |

y'=-y , y0=-2, y 0.5=?
X | y | yn+1=yn+h(f(xn, yn)) |
0 | -2 | |
0.1 | -1.8 | |
0.2 | -1.62 | |
0.3 |-1.458 | |
0.4 | -1.3122 | |
0.5 | -1.18098 | |

y'=te3t-2y, y0=0, y 1=?
x | y | yn+1=yn+h(f(xn, yn)) |
0 | 0 | |
0.1 | 0 | |
0.2 | 0.02008 | |
0.3 | 0.09640 | |0.4 | 0.25788 | |
0.5 | 0.52767 | |
0.6 | 0.92427 | |
0.7 | 1.46249 | |
0.8 | 2.15418 | |
0.9 | 3.00881 | |
1.0 | 4.03397 | |

RUNGE-KUTTA

y'=-y , y0=-2, y0.5=?
x | K1 | K2 | K3 | K4 | Y |
0 | - | - | - | - | -2 |
0.1 | 2 | 1.9 | 1.905 | 1.8095 | -1.99854 |
0.2 | 1.99845 | 1.97352 | 1.97320 | 1.80122 | -1.99711 |
0.3 | 1.99711 | 1.97207 | 1.97175| 1.97175 | -1.99570 |
0.4 | 1.99570 | 1.89591 | 1.96932 | 1.79868 | -1.99425 |
0.5 | 1.99425 | 1.96917 | 1.968850 | 1.79736 | -1.99258 |

y'=x+y, y0=1, y1=?

x | K1 | K2 | K3 | K4 |y |
0 | - | - | - | - | 1 |
0.1 | 1 | 1.1 | 1.055 | 1.3055 | 1.0025 |
0.2 | 1.1025 | 1.19785 | 1.19424 | 1.32194 | 1.0048 |
0.3 | 1.2048 | 1.2963 | 1.3196 | 1.4207 | 1.0069 |
0.4 | 1.3069...