ejercicio 1
27
Ejercicio 6.5.1 Método de Euler (versión completa) Calcular el valor de y cuando x = de la ecuación di!erencial y(") = 1 #olución $nal%tica& Método de Euler 1ero& El incremento es '=".5 onde& con '= ".5 i xi yi !(xi yi) yi*1 " "."""" 1."""" +.5""" 5.,5"" 1 ".5""" 5.,5"" 1.,5"" 5.+-5" Error a soluto en porcentaje& , 1."""" 5.+-5" /1.5""" 5.1,5" 0 1.5""" 5.1,5" /1.,5"" .5""" ,."""" .5""" ".5""" .-5"" 5 ,.5""" .-5"" ,.,5"" 5.+-5" 6 0."""" 5.+-5" ,.5""" -.1,5" - 0.5""" -.1,5" /".,5"" -."""" + ."""" -."""" ,do& El incremento es '="."1 con '= "."1 comparación de resultados i " "."""" 1."""" +.5""" 1."+5" "."" 1."""" 1."""" 1."""" 1 "."1"" 1."+5" +.0"1, 1.16+" "."1 1."+5" 1."+" , ".","" 1.16+" +.1"+ 1., 1 ".", 1.16+" 1.166" 0 "."0"" 1., 1 -. 1"- 1.0,+, "."0 1., 1 1.,61 ".""" 1.0,+, -.-1 1 1."5 "." 1.0,+, 1.0,0 5 "."5"" 1."5 -.5, + 1.+"- "."5 1."5 1.""5 6 "."6"" 1.+"- -.0,+ 1.551 "."6 1.+"- 1.- - "."-"" 1.551 -.15+1 1.6,5- "."- 1.551 1.5- + "."+"" 1.6,5- 6. -5+ 1.6 5 "."+ 1.6,5- 1.61+" "." "" 1.6 5 6.- 5- 1.-60 "." 1.6 5 1.6+6 1" ".1""" 1.-60 6.61+" 1.+, 6 ".1" 1.-60 1.-5" 11 ".11"" 1.+, 6 6.,5 1.+ " ".11 1.+, 6 1.+1 0 1, ".1,"" 1.+ " 6.,6 0 1. 56- ".1, 1.+ " 1.++,+ 10 ".10"" 1. 56- 6." + ,."1-- ".10 1. 56- 1. 6 1 ".1"" ,."1-- 5. , - ,."--" ".1 ,."1-- ,.""+ 15 ".15"" ,."--" 5.-600 ,.106 ".15 ,."--" ,."60, 16 ".16"" ,.106 5.5 " ,.1 "6 ".16 ,.106 ,.1,"1 1- ".1-"" ,.1 "6 5.0-" ,.,5" ".1- ,.1 "6 ,.1-5, 1+ ".1+"" ,.,5" 5.,--1 ,., -- ".1+ ,.,5" ,.,,++ 1 ".1 "" ,., -- 5.11 5 ,.0+ ".1 ,., -- ,.,+"+ ," ".,""" ,.0+ . 6" ,.0 +6 ".," ,.0+ ,.001, ,1 ".,1"" ,.0 +6 .+1"- ,.6- ".,1 ,.0 +6 ,.0+"1 ,, ".,,"" ,.6- .65 5 ,. 00 ".,, ,.6- ,.,- dy2dx = /,x 0 *1,x , /,"x*+.5 y = /x 2,*x 0 /1"x , *+.5x*1 Y i+1 =y i +Φh Φ=f(x i ,y i ) E a %=( x i y i !(x i y i ) y i*1 x i y i '=".5 y i '="."1 y i anal%tica
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Transcript of ejercicio 1
completoEjercicio 6.5.1Mtodo de Euler (versin completa)Calcular el valor de y cuando x = 4 de la ecuacin diferencialdy/dx = -2x3+12x2-20x+8.5y(0) = 1Solucin Analtica:y = -x4/2+4x3-10x2+8.5x+1Mtodo de Euler1ero:El incremento es h=0.5Yi+1=yi+hDonde:=f(xi,yi)con h= 0.5ixiyif(xi,yi)yi+100.00001.00008.50005.250010.50005.25001.25005.8750Error absoluto en porcentaje:21.00005.8750-1.50005.1250Ea%=(yianaltoco-yiaproximado)*100%/ yianaltoco31.50005.1250-1.25004.500042.00004.50000.50004.750052.50004.75002.25005.875063.00005.87502.50007.125073.50007.1250-0.25007.000084.00007.00002do:El incremento es h=0.01con h= 0.01comparacin de resultadoscomparacin de resultadosixiyif(xi,yi)yi+1xiyi h=0.5yi h=0.01yi analticaxi%Error h=0.5%Error h=0.01xiyi h=0.5yi h=0.01yi analticaxi%Error h=0.5%Error h=0.0100.00001.00008.50001.08500.001.00001.00001.00000.000.000.000.001.00001.00001.00000.000.000.0010.01001.08508.30121.16800.011.08501.08400.010.090.252.58202.56050.250.8420.02001.16808.10481.24910.021.16801.16600.020.170.505.25003.25513.21880.5063.111.1330.03001.24917.91071.32820.031.24911.24610.030.240.753.32493.27930.751.3940.04001.32827.71911.40540.041.32821.32430.040.301.005.87503.05023.00001.0095.831.6750.05001.40547.52981.48070.051.40541.40050.050.351.252.64282.59181.251.9760.06001.48077.34281.55410.061.48071.47490.060.391.505.12502.26772.21881.50130.992.2170.07001.55417.15811.62570.071.55411.54740.070.431.752.04311.99801.752.2580.08001.62576.97581.69540.081.62571.61800.080.472.004.50002.04312.00002.00125.002.1690.09001.69546.79571.76340.091.69541.68690.090.512.252.28342.24802.251.57100.10001.76346.61801.82960.101.76341.75400.100.542.504.75002.75022.71882.5074.711.16110.11001.82966.44251.89400.111.82961.81930.110.572.753.37123.34182.750.88120.12001.89406.26931.95670.121.89401.88280.120.593.005.87504.03024.00003.0046.880.75130.13001.95676.09842.01770.131.95671.94460.130.623.254.56404.52933.250.77140.14002.01775.92972.07700.142.01772.00480.140.643.507.12504.76264.71883.5050.990.93150.15002.07705.76332.13460.152.07702.06320.150.663.754.36924.31053.751.36160.16002.13465.59902.19060.162.13462.12010.160.694.007.00003.08003.00004.00133.332.67170.17002.19065.43702.24500.172.19062.17520.170.71180.18002.24505.27712.29770.182.24502.22880.180.72190.19002.29775.11952.34890.192.29772.28080.190.74200.20002.34894.96402.39860.202.34892.33120.200.76210.21002.39864.81072.44670.212.39862.38010.210.78220.22002.44674.65952.49330.222.44672.42740.220.79230.23002.49334.51052.53840.232.49332.47330.230.81240.24002.53844.36362.58200.242.53842.51760.240.82250.25002.58204.21882.62420.252.58202.56050.250.84260.26002.62424.07602.66490.262.62422.60200.260.85270.27002.66493.93542.70430.272.66492.64210.270.87280.28002.70433.79692.74230.282.70432.68070.280.88290.29002.74233.66042.77890.292.74232.71800.290.89300.30002.77893.52602.81410.302.77892.75400.300.91310.31002.81413.39362.84810.312.81412.78850.310.92320.32002.84813.26332.88070.322.84812.82180.320.93330.33002.88073.13492.91210.332.88072.85380.330.94340.34002.91213.00862.94210.342.91212.88450.340.95350.35002.94212.88432.97100.352.94212.91400.350.97360.36002.97102.76192.99860.362.97102.94220.360.98370.37002.99862.64153.02500.372.99862.96920.370.99380.38003.02502.52313.05020.383.02502.99510.381.00390.39003.05022.40663.07430.393.05023.01970.391.01400.40003.07432.29203.09720.403.07433.04320.401.02410.41003.09722.17943.11900.413.09723.06560.411.03420.42003.11902.06863.13970.423.11903.08680.421.04430.43003.13971.95983.15930.433.13973.10690.431.05440.44003.15931.85283.17780.443.15933.12600.441.07450.45003.17781.74783.19530.453.17783.14400.451.08460.46003.19531.64453.21180.463.19533.16100.461.09470.47003.21181.54323.22720.473.21183.17690.471.10480.48003.22721.44363.24160.483.22723.19180.481.11490.49003.24161.34593.25510.493.24163.20580.491.12500.50003.25511.25003.26760.505.25003.25513.21880.5063.111.13510.51003.26761.15593.27910.513.26763.23080.511.14520.52003.27911.06363.28980.523.27913.24190.521.15530.53003.28980.97303.29950.533.28983.25210.531.16540.54003.29950.88433.30840.543.29953.26130.541.17550.55003.30840.79733.31630.553.30843.26970.551.18560.56003.31630.71203.32340.563.31633.27730.561.19570.57003.32340.62843.32970.573.32343.28400.571.20580.58003.32970.54663.33520.583.32973.28990.581.21590.59003.33520.46643.33990.593.33523.29490.591.22600.60003.33990.38803.34370.603.33993.29920.601.23610.61003.34370.31123.34690.613.34373.30270.611.24620.62003.34690.23613.34920.623.34693.30540.621.25630.63003.34920.16273.35080.633.34923.30740.631.26640.64003.35080.09093.35180.643.35083.30870.641.27650.65003.35180.02073.35200.653.35183.30920.651.28660.66003.3520-0.04783.35150.663.35203.30910.661.29670.67003.3515-0.11473.35030.673.35153.30830.671.31680.68003.3503-0.18013.34850.683.35033.30680.681.32690.69003.3485-0.24383.34610.693.34853.30470.691.33700.70003.3461-0.30603.34300.703.34613.30200.701.34710.71003.3430-0.36663.33940.713.34303.29860.711.35720.72003.3394-0.42573.33510.723.33943.29460.721.36730.73003.3351-0.48323.33030.733.33513.29010.731.37740.74003.3303-0.53923.32490.743.33033.28500.741.38750.75003.3249-0.59383.31900.753.32493.27930.751.39760.76003.3190-0.64683.31250.763.31903.27310.761.40770.77003.3125-0.69833.30550.773.31253.26640.771.41780.78003.3055-0.74833.29800.783.30553.25910.781.42790.79003.2980-0.79693.29000.793.29803.25140.791.43800.80003.2900-0.84403.28160.803.29003.24320.801.44810.81003.2816-0.88973.27270.813.28163.23450.811.46820.82003.2727-0.93393.26340.823.27273.22540.821.47830.83003.2634-0.97683.25360.833.26343.21590.831.48840.84003.2536-1.01823.24340.843.25363.20590.841.49850.85003.2434-1.05833.23280.853.24343.19550.851.50860.86003.2328-1.09693.22190.863.23283.18470.861.51870.87003.2219-1.13423.21050.873.22193.17360.871.52880.88003.2105-1.17013.19880.883.21053.16200.881.538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completo
yi h=0.5yi h=0.01yi analticaGRAFICA POR LOS INCREMENTOS DISTINTOS
%Error h=0.5%Error h=0.01ERRORES ABSOLUTAS
