Practica Santa Marta (GEOLOGIA) " YAIR PARRA_YORELY CORENA_LUIS GARCIA_JOSSYMAR PEREZ"
metodos numericos JUAREZ ATITLAN YAIR EVERARDO... ROLDAN SANCHEZ MARIO.xlsx
Transcript of metodos numericos JUAREZ ATITLAN YAIR EVERARDO... ROLDAN SANCHEZ MARIO.xlsx
RAIZ CUADRADASOLUCION DE RAIZ CUADRADA POR METODOS NUMERICOSHALLAR LA RAIZ CUADRADA DE15534BASE60ALTURA258.9ITBASEALTURAAPROX NUEVA BASEEREL APROX160258.9159.4502159.4597.4224128.436224.14723128.4362120.9472124.69173.0034124.6917124.5793124.63550.04515124.6355124.6354124.635506124.6355124.6354124.635507124.6355124.6354124.635508124.6355124.6354124.635509124.6355124.6354124.6355010124.6355124.6354124.6355011124.6355124.6354124.63550
SERIE DE MACLAURI (e^X)CALCULA LASERIA DE MAQCLAURIN MEDIANTE METODOS NUMERICOSe0.5ITAPROX e*EREL APROX0.51100.521.533.33330.531.6257.69230.541.64581.26380.551.64840.15770.561.64870.01820.571.648700.581.648700.591.648700.5101.648700.5111.648700.5121.648700.5131.648700.5141.648700.5151.648700.5161.648700.5171.648700.5181.648700.5191.648700.5201.648700.5211.648700.5221.648700.5231.648700.5241.648700.5251.648700.5261.648700.5271.648700.5281.648700.5291.648700.5301.648700.5311.64870
BISECCIONHALLA LA RAIZ DE F(X)=e^X-X MEDIANTE EL METODO DE LA BISECCION F(X)=e^X-XXF(X)XL=0-5153.4132XU=1-458.5982-323.0855-29.3891ITXLXUF(XL)F(XU)F(XR)XREREL APROX-13.71831011-0.63210.10650.50XL=0120.510.1065-0.6321-0.27760.7533.3333XU=1-0.632130.50.750.1065-0.2776-0.08970.625202-1.864740.50.6250.1065-0.08970.00730.562511.11113-2.950250.56250.6250.0073-0.0897-0.04160.59385.27114-3.981760.56250.59380.0073-0.0416-0.01730.57822.6985-4.993370.56250.57820.0073-0.0173-0.00510.57041.367580.56250.57040.0073-0.00510.0010.56650.688490.56650.57040.001-0.0051-0.00210.56850.3518100.56650.56850.001-0.0021-0.00060.56750.1762110.56650.56750.001-0.00060.00020.5670.0882120.5670.56750.0002-0.0006-0.00020.56730.0529130.5670.56730.0002-0.0002-0.00010.56720.0176140.5670.56720.0002-0.00010.00010.56710.0176150.56710.56720.0001-0.0001-0.00010.56720.0176160.56710.56720.0001-0.0001-0.00010.56720170.56710.56720.0001-0.0001-0.00010.56720
REGLA FALSAHALLA LA RAIZ DE F(X)=e^X-X MEDIANTE EL METODO DE LA BISECCION F(X)=e^X-XXF(X)XL=0-5153.4132XU=1-458.5982-323.0855-29.3891ITXLXUF(XL)F(XU)F(XR)XREREL APROX-13.71831011-0.6321-0.07080.61270XL=01200.61271-0.0708-0.00790.57227.0779XU=1-0.6321300.57221-0.0079-0.00090.56770.79272-1.8647400.56771-0.0009-0.00010.56720.08823-2.9502500.56721-0.00010.00010.56710.01764-3.981760.56710.56720.0001-0.0001-0.00010.56720.01765-4.993370.56710.56720.0001-0.0001-0.00010.5672080.56710.56720.0001-0.0001-0.00010.5672090.56710.56720.0001-0.0001-0.00010.56720100.56710.56720.0001-0.0001-0.00010.56720110.56710.56720.0001-0.0001-0.00010.56720120.56710.56720.0001-0.0001-0.00010.56720130.56710.56720.0001-0.0001-0.00010.56720140.56710.56720.0001-0.0001-0.00010.56720150.56710.56720.0001-0.0001-0.00010.56720160.56710.56720.0001-0.0001-0.00010.56720170.56710.56720.0001-0.0001-0.00010.56720
PUNTO FIJOF(X)=e^X-X
X1=0ITX1EREL APROX0001110020.3679171.81330.692246.850640.500538.301750.606217.436560.545411.147870.57965.900680.56013.481590.57121.9433100.56481.1331110.56850.6508120.56640.3708130.56760.2114140.56690.1235150.56730.0705160.56710.0353170.56720.0176180.56710.0176190.56720.0176
NEWTON RAPSONF(X)=e^X-XF`(X)=-e^X-1X1=0ITX1EREL APROX00010.510020.433715.287130.43620.573140.43610.022950.4361060.4361070.4361080.43610
jacobiX1+3X2-X3=6DESPEJE4X1-X2+X3=5X1=5+X2-X3/4X1+X2-7X3=-9X2=6-X1+X3/3REACOMODANDOX3=-9-X1-X2/-74X1-X2+X3=5X1+3X2-X3=6X1+X2-7X3=-9VECTOR SOLUCION INICIALITX1X2X3EREL APROX DE X1EREL APROX DE X2EREL APROX DE X3000000011.2521.285710010010021.42862.01191.7512.50170.591526.531431.31552.10711.77728.59754.51811.530541.33252.15391.77471.27582.17280.140951.34482.14741.78380.91460.30270.510161.34092.14631.78460.29080.05130.044871.34042.14791.78390.03730.07450.039281.3412.14781.7840.04470.00470.005691.3412.14771.784100.00470.0056101.34092.14771.78410.007500111.34092.14771.7841000121.34092.14771.7841000131.34092.14771.7841000141.34092.14771.7841000151.34092.14771.7841000161.34092.14771.7841000171.34092.14771.7841000181.34092.14771.7841000191.34092.14771.7841000201.34092.14771.7841000211.34092.14771.7841000221.34092.14771.7841000231.34092.14771.7841000241.34092.14771.7841000251.34092.14771.7841000261.34092.14771.7841000271.34092.14771.7841000281.34092.14771.7841000291.34092.14771.7841000301.34092.14771.7841000311.34092.14771.7841000321.34092.14771.7841000331.34092.14771.7841000341.34092.14771.7841000351.34092.14771.7841000361.34092.14771.7841000
GAUSS-SEIDELX1+3X2-X3=6DESPEJE4X1-X2+X3=5X1=5+X2-X3/4X1+X2-7X3=-9X2=6-X1+X3/3REACOMODANDOX3=-9-X1-X2/-74X1-X2+X3=5X1+3X2-X3=6X1+X2-7X3=-9VECTOR SOLUCION INICIALITX1X2X3EREL APROX DE X1EREL APROX DE X2EREL APROX DE X3000000011.251.58331.690510010010021.22322.15581.76842.19126.55634.405131.34692.14051.78399.18410.71480.868941.33922.14821.78390.5750.3584051.34112.14761.78410.14170.02790.011261.34092.14771.78410.01490.0047071.34092.14771.784100081.34092.14771.784100091.34092.14771.7841000101.34092.14771.7841000111.34092.14771.7841000121.34092.14771.7841000131.34092.14771.7841000141.34092.14771.7841000151.34092.14771.7841000161.34092.14771.7841000171.34092.14771.7841000181.34092.14771.7841000191.34092.14771.7841000201.34092.14771.7841000211.34092.14771.7841000221.34092.14771.7841000231.34092.14771.7841000241.34092.14771.7841000251.34092.14771.7841000261.34092.14771.7841000271.34092.14771.7841000281.34092.14771.7841000291.34092.14771.7841000301.34092.14771.7841000311.34092.14771.7841000321.34092.14771.7841000331.34092.14771.7841000341.34092.14771.7841000351.34092.14771.7841000361.34092.14771.7841000
NEWTON RAPSON NO LINEAL
Ye^X-2=0d/dxYe^X-2d/dyYe^X-2Ye^Xe^XdxYe^X-2X^2+Y-4=0JF(X)=-JF(X)2x1dyX^2+Y-4
d/dxX^2+Y-4d/dyX^2+Y-422.21677.3891dx0.2167X1=1.9268-0.0732VECTOR SOLUCION INICIAL1JF(X)=-sol0.341dy0.3X2=0.2926-0.0074
ITX1X2EREL APROX DE X1EREL APROX DE X2020.3001.92682.00946.8675dx0.0094X1=1.9257-0.001111.92680.29263.7992.5292JF(X)=-sol21.92570.29150.05710.37740.29263.85361dy0.0052X2=0.2915-0.001131.92570.29150041.92570.29150051.92570.2915001.92571.99976.8599dx-0.0003X1=1.9257061.92570.2915003JF(X)=-sol71.92570.2915000.29153.85141dy-0.0002X2=0.2915081.92570.29150091.92570.291500101.92570.2915001.92571.99976.8599dx-0.0003X1=1.925704JF(X)=-sol0.29153.85141dy-0.0002X2=0.29150
1.92571.99976.8599dx-0.0003X1=1.925705JF(X)=-sol0.29153.85141dy-0.0002X2=0.29150
1.92571.99976.8599dx-0.0003X1=1.925706JF(X)=-sol0.29153.85141dy-0.0002X2=0.29150
1.92571.99976.8599dx-0.0003X1=1.925707JF(X)=-sol0.29153.85141dy-0.0002X2=0.29150
1.92571.99976.8599dx-0.0003X1=1.92578JF(X)=-sol0.29153.85141dy-0.0002X2=0.2915
1.92571.99976.8599dx-0.0003X1=1.92579JF(X)=-sol0.29153.85141dy-0.0002X2=0.2915
1.92571.99976.8599dx-0.0003X1=1.925710JF(X)=-sol0.29153.85141dy-0.0002X2=0.2915
GAUSS-SEIDEL NO LINEALYe^X-2=0d/dxYe^X-2d/dyYe^X-2Ye^Xe^XdxYe^X-2X^2+Y-4=0JF(X)=-JF(X)2x1dyX^2+Y-4
d/dxX^2+Y-4d/dyX^2+Y-4x=(-y+4)^1/2VECTOR SOLUCION INICIALy=2/e^xITX1X2EREL APROX DE X1EREL APROX DE X2020.30011.92350.29223.97712.669421.92560.29160.10910.205831.92570.29150.00520.034341.92570.29150051.92570.29150061.92570.29150071.92570.29150081.92570.29150091.92570.291500101.92570.291500