数值微分和数值积分-总结复习-习题课(陈)课件.ppt

1、hxfhxfxfiihi)()(lim)(0hhxfxfiih)()(lim0hhxfhxfiih20)()(limjijixxxxxfxfij)()(limhxfhxfxfiii)()()(hhxfxfii)()(hhxfhxfii2)()()()(2)()()()(hOfhhxfhxfxfxRiiiii hxhxhOfhhhxfhxfxfxRiiiiii )()()()()()(2262)()()()()()(hOfhhhxfxfxfxRiiiii 2hxxfhxfhxfhxfiiiiiii )(!2)()()(20.1020.0/)5.050.1()20.0(0.1510.0/)00.2

2、50.0()0(ff0.2510.0/)50.100.1()40.0(fnixLxfini,2,1)()(12121111,)(2)()()()(2)()()(iiiiiiiixxfhhxfxfxffhhxfxfxf)()()()(11111 iiiiiiiixfxxxxxfxxxxxLxfiiiiiiiiiixxhhxfxfxxxfxxxfxf 11111,)()()()()()(,)(2)()()()(2)()()(1212211222212 iiiiiiiiiiiiixxxxhxfhxxxxxfhxxxxxfhxxxxxLxf )(3)(3)(4)(21)()(6)()(21)()(3)

3、()(4)(321)(3221222211221 fhxfxfxfhxffhxfxfhxffhxfxfxfhxfiiiiiiiiiiixi1.01.11.2f(xi)0.250000.62267570.2066122)1(1)(xxfhxfxfxfxf2)()(4)(3)(2100670454.71.02206612.06226757.0425.03)0.1(fhxfxfxf2)()()(20121694.01.02206612.025.0)1.1(fhxfxfxfxf2)(3)(4)()(2102354334.41.02206612.036226757.040.1)2.1(f baiidxx

4、lA)()(xf)(xLndxxfba)(dxxLban)(niiixfA0)(43,21,41210 xxx102dxx43,21,41210 xxx32)()()()(10434121414321102010210dxxxdxxxxxxxxxA31)()()()(10432141214341102101201dxxxdxxxxxxxxxA)()()()(433221314132ffffI32)()()()(10214341432141101202102dxxxdxxxxxxxxxA1)(xf1323132xxf)(2121102x21433221314132)()()()(43322131

5、4132ffffI3)(xxf2)(xxf414332213141323333131103102xdxx314332213141322224141104103xdxx4)(xxf5151105104xdxx1923743322131413244431433221314132222102dxx细分插值型求积公式)(xf)(xLndxxfba)(dxxLban)(bababfafabdxxLdxxff)()()()()()(2121T1科特斯系数21211110)()(,CC个插值节点21,n梯形求积公式bababadxxLxfdxxLdxxffR)()()()()(111badxxR)(1 ba

6、dxbxaxf)(!)(2)()()(bafab 123)(xf)(xLndxxfba)(dxxLban)(个插值节点32,n)(三点公式辛普森求积公式)()()()()(bfbafafabfS612646161,64,61)2(2)2(1)2(0 CCCbababadxxLxfdxxLdxxffR)()()()()(222badxxR)(2badxbxbaxaxf)()(!)()(233)()(222bafbaL)()(22添加插值条件bafbaPbadxbxbaxaxffR)()(!)()()(24224辛普森公式截断误差)()()(452880fab 1011)(dxxfI.693147

7、.02ln|)1ln()1(1111)(101010 xxdxdxxfIxxf 11)(75.0)5.00.1(201)()(2)(bfafabfT694444.0)213241(61)()2(4)(6)(bfbafafabfS3)1(2)(xxf 5)4()1(24)(xxf 1666667.0122)(12)()(31 fabfR0083333.0288024)(2880)()()4(52 fabfR分段数值积分复化梯形求积公式 baniniiixxxfxfhdxxfdxxfii10101)()(2)()(1 11)()(2)(2)(niinbfxfafhfT)()(12)()(31baf

8、abfR )()()()(bafhabfnhfRn 231212)()()(11312 ikinkknxxfhfR等分2分段数值积分mn复化辛普森求积公式)()(2)(4)(3)(1011212 mimiiinbfxfxfafhfS)()()()(knkiinfxxfR4152222880)()()()(4522880fabfR),(,)()(222145290ikinkkbxmabhfh)(,)()()()()()()()()()()(bafmabfhabfmhfhfSfImkkn445444514528801809090 xexf)(xexfxf)()()4(1)()(1)4(exfxf1

9、0dxex 1011)(dxxfI8.212n213n521444510288012880emMmabfSfIn)()()(7.3m4m52122233101211212 enMnabfnhfRn)()()(复化梯形公式区间对分复化积分自适应算法)()(21)(2fHfTfTnnn 102/1)()(niinnxfhfH 10sindxxx外推法-复化梯形公式龙贝格积分)(31)(34)(2fTfTfSnnn )(151)(1516)(2fSfSfCnnn )(631)(6364)(2fCfCfRnnn 10dxxxxf)(5.0 01)1()0(21211ffT6380.01312341TT

10、S6036.05.0211212fTT4341,6433.0)()(4341412214ffTT6565.02314342TTS6578.01151215161SSC 6582.0)()(87858381814218ffffTT87858381,6632.04318344TTS6536.02151415162SSC161516131611169167165163161,6636.016T6654.08S6656.04C6658.02R6536.06316364121CCRk 区间等分数TSCR010.5120.6036 0.6380240.6433 0.6565 0.6578380.6582 0.6632 0.6536 0.65364160.6636 0.6654 0.6656 0.66585320.6656 0.6663 0.6663 0.6663