数值分析上机题目

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1、数值分析上机题目1、分别用不动点迭代与Newton法求解方程x-e2x+5=0的正根与负根。2、Useeachofthefollowingmethodstofindasolutionin[0.1,1]accuratetowithin10A-4for600/—550/+200尢$-20x-l=0a.Bisect!onmethodb.Newton〃smethodc.Secantmethodd.MethodofFalsePositione.Muller'smethod3>应JIJNewton法求f(x)的零点，e=10A-6,这里f(x)=x-s

2、in(x)°再川求重根的两种方法求f(X)的零点。4、应用Newton法求f(x)的零点，e=10A-6zf(x)=x-sin(x)再用Steffensen'smethod加I速具收敛。5、用Nevillezs迭代差值算法，对于函数/(%)=,-1

3、3■7£胸f'Zi心fZixifZf'Z013.01.00174.53.0027.74.10.33123.71207.01284.3253.9分236.1294.1364.23245.63303.0-1.5475.74255.8■86.65275.26107.1627.74.1・4・07136.78174.5-0.67

4、approximationsto『J1+（COS⑴）2dxa>DetermineR1,1,R2/1,R3,1/R4,landR5,l,andusetheseapproximationstopredictthevalueoft

5、heintegral.b、DetermineR2,2,R3,3,R4?4‘andR5,5,andmodifyyourprediction.c^DetermineR6,l,R6,2,R6,3,R6,4,R6,5andR6,6,andmodifyyourprediction.d、e、DetermineR7,7,R8,8,R9,9,andR10,10,andmakeafinalprediction.ExplainwhythisintegralcausesdifficultywithRombergintegrationandhowitcanbere

6、formulatedtomoreeasilydetermineanaccurateapproximation.8、分别用1)Eulermethod2)ModifiedEulerMethod3)Runge-KuttaOrderFour求解P264:7a并计算其误差；Giventheinitial-valueproblem:+f+l0

7、z0<=t<=2,y(0)=0.5,Euler'sMethodwithh=0.025,theMod讦iedEulerMethodwithh=0.05,andtheRunge-Kuttafourth-ordermethodwithh=0.1arecomparedatthecommonmeshpointsofthesemethods0.1,0.2,030.4and0.5.Eachofthesetechniquesrequires20functionalevaluationstodeterminethevalueslistedinTable5.8

8、toapproximatey(0.5).Inthisexample,thefourth-ordermethodisclearlysuperior.10、P322Exercise5.91UsetheRunge-Kuttamethodforsystemstoapproximatethesolutionsofthefollowingsystemsoffirst-orderdifferentialequations,andcomparetheresultstotheactualsolutions.A：—+2色_(2广+Q；=+(厂+2f—4)幺"0

9、「51坷（°）=1饥2（°）=1力=0.2actualsolutionsW1(r)=(l/3>5/-(l/3>_/+e2/Iu2(t)=(1/3)0+(2/3)k+t2e2t11