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UNIVERSIDAD NACIONAL DE CAJAMARCA FACULTAD DE INGENIERIA ESCUELA ACADEMICO PROFESIONAL DE INGENIERIA CIVIL

METODO DE EULER Xi xi+1 n h yi

1 10 10 0.9 0

i 0 1 2 3 4 5 6 7 8 9 10

xi 1 1.9 2.8 3.7 4.6 5.5 6.4 7.3 8.2 9.1 10

yi 2 2.64 3.40 4.22 5.06 5.92 6.79 7.66 8.54 9.42 10.31

ye = yi + h*(√(x/y)) 2.64 3.40 4.22 5.06 5.92 6.79 7.66 8.54 9.42 10.31 11.19

GRAFICO

Chart Title 12 y = 0.0092x2 + 0.7318x + 1.1791 R² = 0.9998

10 8 6 4 2 0 1

1.9

2.8

3.7

4.6

5.5

6.4

7.3

8.2

9.1

10

UNIVERSIDAD NACIONAL DE CAJAMARCA FACULTAD DE INGENIERIA ESCUELA ACADEMICO PROFESIONAL DE INGENIERIA CIVIL

METODO DE HEUM xi xi-1 n h yi

1 10 10 0.9 1

i 0 1 2 3 4 5 6 7 8 9 10

xi 1 1.9 2.8 3.7 4.6 5.5 6.4 7.3 8.2 9.1 10

yi ye = yi + h*(√(x/y)) 2.00000 2.636396 2.70022 3.455169 3.48279 4.289759 4.30420 5.138641 5.14718 5.998000 6.00350 6.864937 6.86872 7.737465 7.74018 8.614218 8.61625 9.494240 9.49580 10.376846 10.37808 11.261532

yh=yi + (h/2)*(√(xi+1/yi)+√(xi+1/ye)) 2.700216 3.482788 4.304197 5.147181 6.003505 6.868715 7.740184 8.616249 9.495802 10.378077 10.819805

GRAFICO 12.00000 10.00000

y = 0.0073x2 + 0.7579x + 1.1817 R² = 0.9999

8.00000 6.00000 4.00000 2.00000 0.00000 1

1.9

2.8

3.7

4.6

5.5

6.4

7.3

8.2

9.1

10

UNIVERSIDAD NACIONAL DE CAJAMARCA FACULTAD DE INGENIERIA ESCUELA ACADEMICO PROFESIONAL DE INGENIERIA CIVIL

METODO DE RUNGE KUTTA

xi xi-1 n h yi

1 10 10 0.9 1

iteracion 0 1 2 3 4 5 6 7 8 9 10

xi 1 1.9 2.8 3.7 4.6 5.5 6.4 7.3 8.2 9.1 10

yi 2 2.98 4.18 5.54 7.04 8.66 10.39 12.22 14.15 16.17 18.28

k1

k2

k3

k4

0.64 0.72 0.74 0.74 0.73 0.72 0.71 0.70 0.69 0.68

0.95666095 1.27427391 1.52723192 1.74548928 1.94045411 2.11823214 2.28263113 2.4362343 2.58089285 2.7179871

1.16971101 1.44102821 1.66747736 1.86791567 2.04992185 2.21779359 2.37434398 2.52155663 2.6608978 2.79348877

1.00317819 1.03744735 1.03376994 1.02081205 1.00596736 0.99143211 0.97786049 0.9653941 0.95399755 0.9435783