h080503.txt

(有源代码)数值分析作业,本文主要包括两个部分,第一部分是常微分方程(ODE)的三个实验题,第二部分是有关的拓展讨论,包括高阶常微分的求解和边值问题的求解(BVP).文中的算法和算例都是基于Matla

dir

.                      adams_wjl.m            nm_ch_0501.m           
..                     cd_temp.m              p51solution.emf        
1.fig                  cd_work.m              p51solutionA50.emf     
2.fig                  d080501.txt            p51solutionA50Ylim.emf 
3.fig                  errorbar.emf           p51solutionYlim.emf    
4.fig                  exact51.m              rk51test.m             
5.fig                  exact52.m              rk_ex_5_1.m            
6.fig                  funtest1.m             rk_wjl.asv             
RK1.m                  funtest3.m             rk_wjl.m               
Thumbs.db              h080503.txt            
a50step001008.emf      history080501.m        
adams_wjl.asv          nm_ch_0501.asv         

open  rk51test
disp(sprintf('%d',feature('SessionTool')))
0
;
dbstatus

dbstack
dbstack
;
disp(which('rk51test'));
e:\matlabtemp\rk51test.m
mdbstatus 'e:\matlabtemp\rk51test.m'
rk51test
       +0.000000000000000
       -0.000283770700128
       -0.000935637052796
       -0.002313707941826
       -0.005085774980601
       -0.010480379817063
       -0.020733285945226
       -0.039877212925475
       -0.075132288169215
       -0.139344236539571
       -0.255244489293290
       -0.462869893886250
       -0.832448491637535
       -1.486720581614691
       -2.639513665649702
       -4.662265667370093
       -8.198523022865629
      -14.360661330538278
      -25.067320056847166
      -43.621328205526879
      -75.698132249763148
     -131.034105500439180
     -226.306808905232170
     -390.043157418767810
     -670.974410761060430
    -1152.244421349023500
    -1975.549172983795900
    -3382.113297836622200
    -5782.189383360557300
    -9872.841671325499200
   -16837.411426979583000
   -28683.071747676469000
   -48811.689594151452000
   -82984.637369174510000
  -140952.433072973040000
  -239205.744248159230000
  -405616.825985170900000
  -687266.361997380850000
 -1163635.237271219500000
 -1968828.008943915400000
 -3328994.434233903900000
 -5625314.929861187900000
 -9499968.880632400500000
-16034346.215980530000000
-27048637.123253345000000
-45605280.986104012000000
-76854688.359474182000000
-129455440.039115910000000
-217958393.881896970000000
-366807626.647239690000000
-617052615.660644530000000
-1037605551.825637800000000
-1744116026.865325900000000
-2930608591.339172400000000
-4922498917.883422900000000
-8265411511.688720700000000
-13873937734.497314000000000
-23280724613.908691000000000
-39053463559.858887000000000
-65492791322.902344000000000
-109800082500.949220000000000
-184031081871.550780000000000
-308363497582.250000000000000
-516561165453.140620000000000
-865109555811.640620000000000
-1448486407903.234400000000000
-2424682827978.687500000000000
-4057847658162.375000000000000
-6789531134372.000000000000000
-11357687076491.125000000000000
-18995414994616.000000000000000
-31762818552961.500000000000000
-53101051542012.500000000000000
-88757165845823.000000000000000
-148327688146004.000000000000000
-247834472664200.000000000000000
-414022542294584.000000000000000
-691530064621656.000000000000000
-1154848168563712.000000000000000
-1928267697731488.000000000000000
-3219142266463104.000000000000000
-5373350271842816.000000000000000
-8967759154702592.000000000000000
-14964359317716864.000000000000000
-24967167465024256.000000000000000
-41650370385995264.000000000000000
-69471767501566976.000000000000000
-115861489056854020.000000000000000
-193202384616775680.000000000000000
-322128963453923330.000000000000000
-537022197263671300.000000000000000
-895160850858254340.000000000000000
-1491961020848734200.000000000000000
-2486351699871006700.000000000000000
-4143023809607958500.000000000000000
-6902765907646808100.000000000000000
-11499547168060604000.000000000000000
-19155399191088464000.000000000000000
-31904762510927987000.000000000000000
-53134256023870636000.000000000000000
-88480869022534992000.000000000000000
        1.000000000000000
        0.098373740284549
        0.160337594332044
        0.240006202870579
        0.320000113969933
        0.400000002094054
        0.480000000038476
        0.560000000000707
        0.640000000000013
        0.720000000000000
        1.000000000000000
        5.079999999999999
       25.159999999999993
      125.239999999999880
      625.320000000000050
     3125.400000000002400
    15625.479999999978000
    78125.559999999707000
   390625.639999997740000
  1953125.719999996900000
        1.000000000000000
        0.098315638888734
        0.160335462627903
        0.240006144212353
        0.320000112535175
        0.400000002061154
        0.480000000037751
        0.560000000000692
        0.640000000000013
        0.720000000000000
figure(7)
plot(x5,y5,x6,y6)
title('\alpha=-50,step with 0.01 and 0.08')
ylim([-1,50])
legend('step 0.01','step 0.08')

figure(7)
plot(x5,y5,x6,y6)
title('\alpha=-50,step with 0.01 and 0.08')
ylim([-1,50])
legend('step 0.01','step 0.08')
xlabel('x')
ylabel('y')
xlabel('x')
ylabel('y')
disp(which('rk51test'));
e:\matlabtemp\rk51test.m
clear 'e:\matlabtemp\rk51test.m'
rk51test
       +0.000000000000000
       -0.000283770700128
       -0.000935637052796
       -0.002313707941826
       -0.005085774980601
       -0.010480379817063
       -0.020733285945226
       -0.039877212925475
       -0.075132288169215
       -0.139344236539571
       -0.255244489293290
       -0.462869893886250
       -0.832448491637535
       -1.486720581614691
       -2.639513665649702
       -4.662265667370093
       -8.198523022865629
      -14.360661330538278
      -25.067320056847166
      -43.621328205526879
      -75.698132249763148
     -131.034105500439180
     -226.306808905232170
     -390.043157418767810
     -670.974410761060430
    -1152.244421349023500
    -1975.549172983795900
    -3382.113297836622200
    -5782.189383360557300
    -9872.841671325499200
   -16837.411426979583000
   -28683.071747676469000
   -48811.689594151452000
   -82984.637369174510000
  -140952.433072973040000
  -239205.744248159230000
  -405616.825985170900000
  -687266.361997380850000
 -1163635.237271219500000
 -1968828.008943915400000
 -3328994.434233903900000
 -5625314.929861187900000
 -9499968.880632400500000
-16034346.215980530000000
-27048637.123253345000000
-45605280.986104012000000
-76854688.359474182000000
-129455440.039115910000000
-217958393.881896970000000
-366807626.647239690000000
-617052615.660644530000000
-1037605551.825637800000000
-1744116026.865325900000000
-2930608591.339172400000000
-4922498917.883422900000000
-8265411511.688720700000000
-13873937734.497314000000000
-23280724613.908691000000000
-39053463559.858887000000000
-65492791322.902344000000000
-109800082500.949220000000000
-184031081871.550780000000000
-308363497582.250000000000000
-516561165453.140620000000000
-865109555811.640620000000000
-1448486407903.234400000000000
-2424682827978.687500000000000
-4057847658162.375000000000000
-6789531134372.000000000000000
-11357687076491.125000000000000
-18995414994616.000000000000000
-31762818552961.500000000000000
-53101051542012.500000000000000
-88757165845823.000000000000000
-148327688146004.000000000000000
-247834472664200.000000000000000
-414022542294584.000000000000000
-691530064621656.000000000000000
-1154848168563712.000000000000000
-1928267697731488.000000000000000
-3219142266463104.000000000000000
-5373350271842816.000000000000000
-8967759154702592.000000000000000
-14964359317716864.000000000000000
-24967167465024256.000000000000000
-41650370385995264.000000000000000
-69471767501566976.000000000000000
-115861489056854020.000000000000000
-193202384616775680.000000000000000
-322128963453923330.000000000000000
-537022197263671300.000000000000000
-895160850858254340.000000000000000
-1491961020848734200.000000000000000
-2486351699871006700.000000000000000
-4143023809607958500.000000000000000
-6902765907646808100.000000000000000
-11499547168060604000.000000000000000
-19155399191088464000.000000000000000
-31904762510927987000.000000000000000
-53134256023870636000.000000000000000
-88480869022534992000.000000000000000
        1.000000000000000
        0.098373740284549
        0.160337594332044
        0.240006202870579
        0.320000113969933
        0.400000002094054
        0.480000000038476
        0.560000000000707
        0.640000000000013
        0.720000000000000
        1.000000000000000
        5.079999999999999
       25.159999999999993
      125.239999999999880
      625.320000000000050
     3125.400000000002400
    15625.479999999978000
    78125.559999999707000
   390625.639999997740000
  1953125.719999996900000
        1.000000000000000
        0.098315638888734
        0.160335462627903
        0.240006144212353
        0.320000112535175
        0.400000002061154
        0.480000000037751
        0.560000000000692
        0.640000000000013
        0.720000000000000
fprintf('%25.15f\n',x5)

fprintf('%25.15f\n',x5)
        0.000000000000000
        0.010000000000000
        0.020000000000000
        0.030000000000000
        0.040000000000000
        0.050000000000000
        0.060000000000000
        0.070000000000000
        0.080000000000000
        0.090000000000000
        0.100000000000000
        0.110000000000000
        0.120000000000000
        0.130000000000000
        0.140000000000000
        0.150000000000000
        0.160000000000000
        0.170000000000000
        0.180000000000000
        0.190000000000000
        0.200000000000000
        0.210000000000000
        0.220000000000000
        0.230000000000000
        0.240000000000000
        0.250000000000000
        0.260000000000000
        0.270000000000000
        0.280000000000000
        0.290000000000000
        0.300000000000000
        0.310000000000000
        0.320000000000000
        0.330000000000000
        0.340000000000000
        0.350000000000000
        0.360000000000000
        0.370000000000000
        0.380000000000000
        0.390000000000000
        0.400000000000000
        0.410000000000000
        0.420000000000000
        0.430000000000000
        0.440000000000000
        0.450000000000000
        0.460000000000000
        0.470000000000000
        0.480000000000000
        0.490000000000000
        0.500000000000000
        0.510000000000000
        0.520000000000000
        0.530000000000000
        0.540000000000000
        0.550000000000000
        0.560000000000000
        0.570000000000000
        0.580000000000000
        0.590000000000000
        0.600000000000000
        0.610000000000000
        0.620000000000000
        0.630000000000000
        0.640000000000000
        0.650000000000000
        0.660000000000000
        0.670000000000000
        0.680000000000000
        0.690000000000000
        0.700000000000000
        0.710000000000000
        0.720000000000000
        0.730000000000000
        0.740000000000000
        0.750000000000000
        0.760000000000000
        0.770000000000000
        0.780000000000000
        0.790000000000000
        0.800000000000000
        0.810000000000000
        0.820000000000000
        0.830000000000000
        0.840000000000000
        0.850000000000000
        0.860000000000000
        0.870000000000000
        0.880000000000000
        0.890000000000000
        0.900000000000000
        0.910000000000000
        0.920000000000000
        0.930000000000000
        0.940000000000000
        0.950000000000000
        0.960000000000000
        0.970000000000000
        0.980000000000000
        0.990000000000000
        1.000000000000000
fprintf('%25.15f\n',x5(index))

fprintf('%25.15f\n',x5(index))
        0.000000000000000
        0.080000000000000
        0.160000000000000
        0.240000000000000
        0.320000000000000
        0.400000000000000
        0.480000000000000
        0.560000000000000
        0.640000000000000
        0.720000000000000
fprintf('%25.15f\n',y5(index))
fprintf('%25.15f\n',y5(index))
        1.000000000000000
        0.098373740284549
        0.160337594332044
        0.240006202870579
        0.320000113969933
        0.400000002094054
        0.480000000038476
        0.560000000000707
        0.640000000000013
        0.720000000000000
fprintf('%25.15f\n',y6(1:10))
fprintf('%25.15f\n',y6(1:10))
        1.000000000000000
        5.079999999999999
       25.159999999999993
      125.239999999999880
      625.320000000000050
     3125.400000000002400
    15625.479999999978000
    78125.559999999707000
   390625.639999997740000
  1953125.719999996900000
fprintf('%25.15f\n',yy5(index))
fprintf('%25.15f\n',yy5(index))
        1.000000000000000
        0.098315638888734
        0.160335462627903
        0.240006144212353
        0.320000112535175
        0.400000002061154
        0.480000000037751
        0.560000000000692
        0.640000000000013
        0.720000000000000
disp(which('rk51test'));
e:\matlabtemp\rk51test.m
clear 'e:\matlabtemp\rk51test.m'
dbstack
;
disp(which('na52test'));
e:\matlabtemp\na52test.m
clear 'e:\matlabtemp\na52test.m'
disp(which('na52test'));
e:\matlabtemp\na52test.m
clear 'e:\matlabtemp\na52test.m'
dbstack
;
disp(which('funtest3'));
e:\matlabtemp\funtest3.m
mdbstatus 'e:\matlabtemp\funtest3.m'

cc
clf
close all
cc
[x1,y1]=rk_wjl('funtest3',0,2,1,0.01);
[x2,y2]=adams_wjl('funtest3',0,2,1,0.01);
[x1,y1]=rk_wjl('funtest3',0,2,1,0.01);
[x2,y2]=adams_wjl('funtest3',0,2,1,0.01);
disp(which('na52test'));
e:\matlabtemp\na52test.m
clear 'e:\matlabtemp\na52test.m'
cc
tic
[x1,y1]=rk_wjl('funtest3',0,2,1,0.01);
t1=toc

tic
[x2,y2]=adams_wjl('funtest3',0,2,1,0.01);
t2=toc