Análisis numérico resumen
Enviado por Jairo Silva • 27 de Noviembre de 2017 • Tareas • 1.144 Palabras (5 Páginas) • 299 Visitas
[pic 1]
Análisis Numérico
Integrantes: Jairo Bayardo Silva Corea
Sara Cristela Martinez Baquedano
Linda Aura Hernández Pérez
Tema: Problema de valores iniciales y valores de frontera.
Grupo: 2M2Q
Docente: ING. Claudia Martínez
Managua, Nicaragua. Noviembre 22, 2017
PROBLEMAS.
- La concentración de un reactivo varía con el tiempo según la siguiente ecuación:
= -0.07506C[pic 2]
Donde C es la concentración (mol/L) y t el tiempo (minutos). Si al inicio se tiene una concentración de 22 mol/L, resuelva la ecuación en el intervalo de 0 a 25 minutos (use h=0.5). Grafique la solución (C vs t).
Resolución:
Para resolver la ecuación de la variación de la concentración, se plantea las expresiones generales, aplicando el método de Runge-Kutta de cuarto orden:
= -0.07506 c C(0)=22 mol/L h= 0.5 [pic 3]
C k+1 = Ck +1/6(α1, +2 α2, + 2 α3, + α4)
α1 = h (-0.07506 (Ck)
α2 = h [-0.07506 (Ck + α1 / 2)
α3 = h [-0.07506 (Ck + α2 / 2)
α4 = h [-0.07506 (Ck + α3)
Estas son las ecuaciones que usaremos para implementar el método en Excel.
Resolución en Excel:
Se implementó el método de Runge-Kutta 4 para resolver el problema dado, dando como resultado los siguientes datos:
t | C | α1 | α2 | α3 | α4 |
0 | 22 | -0.82566 | -0.81016649 | -0.81045723 | -0.79524354 |
0.5 | 21.1896415 | -0.79524725 | -0.78032443 | -0.78060446 | -0.76595116 |
1 | 20.4091321 | -0.76595473 | -0.75158159 | -0.7518513 | -0.73773775 |
1.5 | 19.6573724 | -0.73774119 | -0.72389747 | -0.72415725 | -0.71056357 |
2 | 18.9333034 | -0.71056688 | -0.69723309 | -0.6974833 | -0.68439033 |
2.5 | 18.2359051 | -0.68439352 | -0.67155087 | -0.67179187 | -0.65918117 |
3 | 17.564195 | -0.65918424 | -0.64681465 | -0.64704676 | -0.63490057 |
3.5 | 16.9172271 | -0.63490353 | -0.62298957 | -0.62321313 | -0.61151434 |
4 | 16.2940899 | -0.61151719 | -0.60004207 | -0.6002574 | -0.58898953 |
4.5 | 15.6939056 | -0.58899228 | -0.57793984 | -0.57814724 | -0.56729441 |
5 | 15.1158288 | -0.56729705 | -0.55665173 | -0.55685149 | -0.54639842 |
5.5 | 14.5590452 | -0.54640096 | -0.53614775 | -0.53634015 | -0.52627212 |
6 | 14.0227703 | -0.52627457 | -0.51639903 | -0.51658434 | -0.50688716 |
6.5 | 13.5062489 | -0.50688952 | -0.49737774 | -0.49755623 | -0.48821624 |
7 | 13.0087533 | -0.48821851 | -0.47905709 | -0.47922901 | -0.47023305 |
7.5 | 12.5295827 | -0.47023524 | -0.46141127 | -0.46157686 | -0.45291226 |
8 | 12.0680621 | -0.45291437 | -0.44441543 | -0.44457491 | -0.43622947 |
8.5 | 11.6235413 | -0.43623151 | -0.42804562 | -0.42819923 | -0.42016119 |
9 | 11.1953942 | -0.42016315 | -0.41227878 | -0.41242673 | -0.40468477 |
9.5 | 10.7830177 | -0.40468666 | -0.39709271 | -0.39723521 | -0.38977842 |
10 | 10.3858309 | -0.38978023 | -0.38246601 | -0.38260326 | -0.37542113 |
10.5 | 10.0032743 | -0.37542288 | -0.36837807 | -0.36851027 | -0.36159269 |
11 | 9.6348089 | -0.36159438 | -0.35480906 | -0.35493639 | -0.34827362 |
11.5 | 9.27991575 | -0.34827524 | -0.34173985 | -0.34186249 | -0.33544514 |
12 | 8.93809491 | -0.3354467 | -0.32915204 | -0.32927016 | -0.32308919 |
12.5 | 8.60886485 | -0.3230907 | -0.3170279 | -0.31714167 | -0.31118837 |
13 | 8.29176182 | -0.31118982 | -0.30535034 | -0.30545992 | -0.29972591 |
13.5 | 7.98633911 | -0.29972731 | -0.29410292 | -0.29420847 | -0.28868566 |
14 | 7.69216648 | -0.28868701 | -0.2832698 | -0.28337145 | -0.27805208 |
14.5 | 7.40882955 | -0.27805337 | -0.2728357 | -0.27293361 | -0.26781017 |
15 | 7.13592919 | -0.26781142 | -0.26278594 | -0.26288024 | -0.25794553 |
15.5 | 6.87308097 | -0.25794673 | -0.25310636 | -0.25319719 | -0.24844424 |
16 | 6.61991463 | -0.2484454 | -0.24378332 | -0.2438708 | -0.23929292 |
16.5 | 6.37607353 | -0.23929404 | -0.23480369 | -0.23488795 | -0.2304787 |
17 | 6.1412142 | -0.23047977 | -0.22615482 | -0.22623597 | -0.22198913 |
17.5 | 5.91500579 | -0.22199017 | -0.21782452 | -0.21790269 | -0.21381228 |
18 | 5.69712964 | -0.21381328 | -0.20980107 | -0.20987636 | -0.20593662 |
18.5 | 5.48727885 | -0.20593758 | -0.20207316 | -0.20214567 | -0.19835105 |
19 | 5.2851578 | -0.19835197 | -0.1946299 | -0.19469974 | -0.19104489 |
19.5 | 5.09048178 | -0.19104578 | -0.18746081 | -0.18752808 | -0.18400785 |
20 | 4.90297655 | -0.18400871 | -0.18055579 | -0.18062058 | -0.17723002 |
20.5 | 4.72237797 | -0.17723085 | -0.17390511 | -0.17396752 | -0.17070184 |
21 | 4.54843165 | -0.17070264 | -0.1674994 | -0.16755951 | -0.16441413 |
21.5 | 4.38089254 | -0.1644149 | -0.16132965 | -0.16138755 | -0.15835802 |
22 | 4.21952466 | -0.15835876 | -0.15538716 | -0.15544292 | -0.15252499 |
22.5 | 4.06410067 | -0.1525257 | -0.14966355 | -0.14971726 | -0.14690681 |
23 | 3.91440165 | -0.14690749 | -0.14415077 | -0.1442025 | -0.14149557 |
23.5 | 3.77021671 | -0.14149623 | -0.13884106 | -0.13889088 | -0.13628366 |
24 | 3.63134275 | -0.13628429 | -0.13372692 | -0.13377491 | -0.13126372 |
24.5 | 3.49758414 | -0.13126433 | -0.12880116 | -0.12884738 | -0.12642869 |
25 | 3.36875246 | -0.12642928 | -0.12405683 | -0.12410135 | -0.12177176 |
...