Eulmod

eulerModificado[1,6,2,0.1] {{1,2},{1.1,2.01168},{1.2,2.23622},{1.3,2.61094},{1.4,3.10834},{1.5,3.7169}, {1.6,4.4329},{1.7,5.25673},{1.8,6.19097},{1.9,7.23951},{2.,8.40698},{2.1,9.69846}, {2.2,11.1194},{2.3,12.6752},{2.4,14.3718},{2.5,16.2148},{2.6,18.2101}, {2.7,20.3636},{2.8,22.6813},{2.9,25.169},{3.,27.8326},{3.1,30.6783},{3.2,33.7118}, {3.3,36.9393},{3.4,40.3666},{3.5,43.9999},{3.6,47.845},{3.7,51.9079},{3.8,56.1947}, {3.9,60.7113},{4.,65.4637},{4.1,70.458},{4.2,75.7},{4.3,81.196},{4.4,86.9517}, {4.5,92.9732},{4.6,99.2666},{4.7,105.838},{4.8,112.693},{4.9,119.837},{5.,127.278}, {5.1,135.02},{5.2,143.071},{5.3,151.435},{5.4,160.118},{5.5,169.128},{5.6,178.469}, {5.7,188.149},{5.8,198.172},{5.9,208.544},{6.,219.273}} solexacta=t3+t-4 {2,2.01401,2.21025,2.54713,3.00431,3.57253,4.24859,5.03273,5.92726,6.93573,8.062 5,9.31242,10.6907,12.2027,13.8541,15.6506,17.5979,19.7018,21.9683,24.4031,27.012 3,29.8018,32.7775,35.9454,39.3115,42.8817,46.662,50.6583,54.8768,59.3233,64.0039, 68.9245,74.0912,79.5099,85.1867,91.1274,97.3382,103.825,110.594,117.651,125.002, 132.652,140.609,148.878,157.465,166.376,175.617,185.194,195.113,205.38,216.001} solaproximada=w {2,2.01168,2.23622,2.61094,3.10834,3.7169,4.4329,5.25673,6.19097,7.23951,8.40698, 9.69846,11.1194,12.6752,14.3718,16.2148,18.2101,20.3636,22.6813,25.169,27.8326,3 0.6783,33.7118,36.9393,40.3666,43.9999,47.845,51.9079,56.1947,60.7113,65.4637,70. 458,75.7,81.196,86.9517,92.9732,99.2666,105.838,112.693,119.837,127.278,135.02,14 3.071,151.435,160.118,169.128,178.469,188.149,198.172,208.544,219.273} Abs[solexacta-solaproximada] {0,0.00233164,0.0259634,0.0638128,0.104034,0.144365,0.184312,0.223995,0.263712, 0.303779,0.344479,0.386044,0.428663,0.472486,0.51763,0.564188,0.612233,0.661824 ,0.713007,0.765818,0.820288,0.87644,0.934293,0.993864,1.05516,1.11821,1.183,1.24 955,1.31786,1.38794,1.4598,1.53343,1.60884,1.68603,1.765,1.84577,1.92832,2.01266, 2.09879,2.18671,2.27643,2.36793,2.46124,2.55634,2.65323,2.75192,2.8524,2.95468,3. 05876,3.16464,3.27231} error=ListPlot[Abs[solexacta-solaproximada],PlotStyle {Green,PointSize[0.02]}]

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aproximacion=ListPlot[eulerModificado[1,6,2,0.1],PlotStylePointSize[0.02]]

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curvaExacta=Plot[t3+1/t4,{t,1,6},PlotStyleRed]

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Show[aproximacion,curvaExacta,error]

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eulerModificado[1,6,2,0.03] {{1,2},{1.03,1.97994},{1.06,1.98192},{1.09,2.00335},{1.12,2.04217},{1.15,2.09672}, {1.18,2.16569},{1.21,2.248},{1.24,2.34281},{1.27,2.44943},{1.3,2.56732}, {1.33,2.69603},{1.36,2.83524},{1.39,2.98467},{1.42,3.14413},{1.45,3.31346}, {1.48,3.49258},{1.51,3.6814},{1.54,3.8799},{1.57,4.08806},{1.6,4.30591}, {1.63,4.53348},{1.66,4.77081},{1.69,5.01797},{1.72,5.27504},{1.75,5.54211}, {1.78,5.81926},{1.81,6.1066},{1.84,6.40424},{1.87,6.71231},{1.9,7.03091}, {1.93,7.36017},{1.96,7.70023},{1.99,8.05122},{2.02,8.41327},{2.05,8.78652}, {2.08,9.17111},{2.11,9.56719},{2.14,9.9749},{2.17,10.3944},{2.2,10.8258}, {2.23,11.2693},{2.26,11.725},{2.29,12.1931},{2.32,12.6737},{2.35,13.167}, {2.38,13.6731},{2.41,14.1923},{2.44,14.7245},{2.47,15.2701},{2.5,15.8291}, {2.53,16.4018},{2.56,16.9882},{2.59,17.5886},{2.62,18.2031},{2.65,18.8318}, {2.68,19.4749},{2.71,20.1325},{2.74,20.805},{2.77,21.4922},{2.8,22.1946}, {2.83,22.9121},{2.86,23.645},{2.89,24.3934},{2.92,25.1576},{2.95,25.9375}, {2.98,26.7335},{3.01,27.5456},{3.04,28.3741},{3.07,29.219},{3.1,30.0806}, {3.13,30.959},{3.16,31.8544},{3.19,32.7669},{3.22,33.6967},{3.25,34.6439}, {3.28,35.6088},{3.31,36.5914},{3.34,37.592},{3.37,38.6107},{3.4,39.6477}, {3.43,40.703},{3.46,41.777},{3.49,42.8697},{3.52,43.9813},{3.55,45.1119}, {3.58,46.2618},{3.61,47.4311},{3.64,48.62},{3.67,49.8285},{3.7,51.057}, {3.73,52.3054},{3.76,53.5741},{3.79,54.8631},{3.82,56.1727},{3.85,57.503}, {3.88,58.854},{3.91,60.2261},{3.94,61.6194},{3.97,63.034},{4.,64.4701}, {4.03,65.9279},{4.06,67.4074},{4.09,68.909},{4.12,70.4327},{4.15,71.9787}, {4.18,73.5471},{4.21,75.1382},{4.24,76.7521},{4.27,78.3889},{4.3,80.0489}, {4.33,81.7321},{4.36,83.4387},{4.39,85.169},{4.42,86.923},{4.45,88.7009}, {4.48,90.503},{4.51,92.3292},{4.54,94.1799},{4.57,96.0551},{4.6,97.9551}, {4.63,99.88},{4.66,101.83},{4.69,103.805},{4.72,105.806},{4.75,107.832}, {4.78,109.883},{4.81,111.961},{4.84,114.065},{4.87,116.195},{4.9,118.351}, {4.93,120.533},{4.96,122.743},{4.99,124.979},{5.02,127.242},{5.05,129.533}, {5.08,131.85},{5.11,134.196},{5.14,136.568},{5.17,138.969},{5.2,141.398},

{5.23,143.854},{5.26,146.34},{5.29,148.853},{5.32,151.395},{5.35,153.966}, {5.38,156.566},{5.41,159.195},{5.44,161.853},{5.47,164.541},{5.5,167.258}, {5.53,170.005},{5.56,172.782},{5.59,175.589},{5.62,178.426},{5.65,181.294}, {5.68,184.192},{5.71,187.121},{5.74,190.081},{5.77,193.072},{5.8,196.094}, {5.83,199.147},{5.86,202.232},{5.89,205.349},{5.92,208.497},{5.95,211.678}, {5.98,214.89}} aproximacion=ListPlot[eulerModificado[1,6,2,0.03],PlotStylePointSize[0.01]]

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eulerModificado[1,6,2,0.025] {{1,2},{1.025,1.9819},{1.05,1.97925},{1.075,1.99053},{1.1,2.01444}, {1.125,2.04993},{1.15,2.09611},{1.175,2.15225},{1.2,2.21773},{1.225,2.29204}, {1.25,2.37476},{1.275,2.46552},{1.3,2.56403},{1.325,2.67006},{1.35,2.7834}, {1.375,2.90389},{1.4,3.03141},{1.425,3.16585},{1.45,3.30713},{1.475,3.4552}, {1.5,3.61002},{1.525,3.77157},{1.55,3.93983},{1.575,4.11481},{1.6,4.29651}, {1.625,4.48496},{1.65,4.68019},{1.675,4.88222},{1.7,5.09111},{1.725,5.3069}, {1.75,5.52963},{1.775,5.75937},{1.8,5.99617},{1.825,6.24011},{1.85,6.49123}, {1.875,6.74961},{1.9,7.01532},{1.925,7.28844},{1.95,7.56903},{1.975,7.85718}, {2.,8.15297},{2.025,8.45646},{2.05,8.76774},{2.075,9.0869},{2.1,9.41401}, {2.125,9.74916},{2.15,10.0924},{2.175,10.4439},{2.2,10.8037},{2.225,11.1719}, {2.25,11.5485},{2.275,11.9337},{2.3,12.3275},{2.325,12.7301},{2.35,13.1415}, {2.375,13.5617},{2.4,13.991},{2.425,14.4294},{2.45,14.877},{2.475,15.3338}, {2.5,15.8},{2.525,16.2756},{2.55,16.7608},{2.575,17.2556},{2.6,17.7602}, {2.625,18.2745},{2.65,18.7988},{2.675,19.3331},{2.7,19.8774},{2.725,20.432}, {2.75,20.9968},{2.775,21.572},{2.8,22.1577},{2.825,22.7539},{2.85,23.3607}, {2.875,23.9783},{2.9,24.6067},{2.925,25.2461},{2.95,25.8964},{2.975,26.5579}, {3.,27.2306},{3.025,27.9145},{3.05,28.6099},{3.075,29.3167},{3.1,30.0351}, {3.125,30.7652},{3.15,31.5071},{3.175,32.2608},{3.2,33.0264},{3.225,33.8041}, {3.25,34.5939},{3.275,35.396},{3.3,36.2103},{3.325,37.0371},{3.35,37.8764}, {3.375,38.7283},{3.4,39.5929},{3.425,40.4702},{3.45,41.3605},{3.475,42.2637}, {3.5,43.18},{3.525,44.1095},{3.55,45.0522},{3.575,46.0082},{3.6,46.9777}, {3.625,47.9608},{3.65,48.9574},{3.675,49.9678},{3.7,50.992},{3.725,52.0301}, {3.75,53.0823},{3.775,54.1485},{3.8,55.2289},{3.825,56.3236},{3.85,57.4326}, {3.875,58.5562},{3.9,59.6943},{3.925,60.847},{3.95,62.0145},{3.975,63.1969}, {4.,64.3942},{4.025,65.6065},{4.05,66.834},{4.075,68.0766},{4.1,69.3346}, {4.125,70.608},{4.15,71.8969},{4.175,73.2014},{4.2,74.5216},{4.225,75.8576}, {4.25,77.2094},{4.275,78.5772},{4.3,79.9611},{4.325,81.3611},{4.35,82.7774}, {4.375,84.2101},{4.4,85.6591},{4.425,87.1247},{4.45,88.6069},{4.475,90.1059},

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{4.5,91.6216},{4.525,93.1543},{4.55,94.704},{4.575,96.2707},{4.6,97.8547}, {4.625,99.4559},{4.65,101.075},{4.675,102.711},{4.7,104.364},{4.725,106.036}, {4.75,107.725},{4.775,109.431},{4.8,111.156},{4.825,112.899},{4.85,114.66}, {4.875,116.439},{4.9,118.237},{4.925,120.053},{4.95,121.887},{4.975,123.74}, {5.,125.612},{5.025,127.502},{5.05,129.412},{5.075,131.34},{5.1,133.287}, {5.125,135.254},{5.15,137.24},{5.175,139.245},{5.2,141.269},{5.225,143.314}, {5.25,145.377},{5.275,147.461},{5.3,149.564},{5.325,151.687},{5.35,153.83}, {5.375,155.994},{5.4,158.177},{5.425,160.381},{5.45,162.605},{5.475,164.849}, {5.5,167.114},{5.525,169.4},{5.55,171.707},{5.575,174.034},{5.6,176.383}, {5.625,178.752},{5.65,181.142},{5.675,183.554},{5.7,185.987},{5.725,188.441}, {5.75,190.917},{5.775,193.415},{5.8,195.934},{5.825,198.475},{5.85,201.038}, {5.875,203.623},{5.9,206.23},{5.925,208.859},{5.95,211.51},{5.975,214.183}, {6.,216.88}} aproximacion=ListPlot[eulerModificado[1,6,2,0.025],PlotStylePointSize[0.001]]

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