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

tic
[x1,y1]=rk_wjl('funtest3',0,2,1,0.01);
t1=toc

t1 =

    0.0300


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

t2 =

    0.0300

tic
[x1,y1]=rk_wjl('funtest3',0,2,1,0.001);
t1=toc

tic
[x2,y2]=adams_wjl('funtest3',0,2,1,0.001);
t2=toc
tic
[x1,y1]=rk_wjl('funtest3',0,2,1,0.001);
t1=toc

t1 =

    0.3910


tic
[x2,y2]=adams_wjl('funtest3',0,2,1,0.001);
t2=toc

t2 =

    0.2400


cc
tic
[x1,y1]=rk_wjl('funtest3',0,2,1,0.001);
t1=toc

tic
[x2,y2]=adams_wjl('funtest3',0,2,1,0.001);
t2=toc

tic
[x1,y1]=rk_wjl('funtest3',0,2,1,0.001);
t1=toc

t1 =

    0.3110


tic
[x2,y2]=adams_wjl('funtest3',0,2,1,0.001);
t2=toc

t2 =

    0.2500

disp(which('na52test'));
e:\matlabtemp\na52test.m
clear 'e:\matlabtemp\na52test.m'
disp(which('na52test'));
e:\matlabtemp\na52test.m
clear 'e:\matlabtemp\na52test.m'
tic
[x1,y1]=rk_wjl('funtest3',0,2,1,0.001);
t1=toc
tic
[x1,y1]=rk_wjl('funtest3',0,2,1,0.001);
t1=toc

t1 =

    1.7320

tic
[x2,y2]=adams_wjl('funtest3',0,2,1,0.001);
t2=toc
tic
[x2,y2]=adams_wjl('funtest3',0,2,1,0.001);
t2=toc

t2 =

    2.4540

tic
[x1,y1]=rk_wjl('funtest3',0,2,1,0.001);
t1=toc
tic
[x1,y1]=rk_wjl('funtest3',0,2,1,0.001);
t1=toc

t1 =

    0.3400

tic
[x2,y2]=adams_wjl('funtest3',0,2,1,0.001);
t2=toc
tic
[x2,y2]=adams_wjl('funtest3',0,2,1,0.001);
t2=toc

t2 =

    0.2600

tic
[x1,y1]=rk_wjl('funtest3',0,2,1,0.001);
t1=toc
tic
[x1,y1]=rk_wjl('funtest3',0,2,1,0.001);
t1=toc

t1 =

    0.3210

tic
[x2,y2]=adams_wjl('funtest3',0,2,1,0.001);
t2=toc
tic
[x2,y2]=adams_wjl('funtest3',0,2,1,0.001);
t2=toc

t2 =

    0.3300

tic
[x2,y2]=adams_wjl('funtest3',0,2,1,0.001);
t2=toc
tic
[x2,y2]=adams_wjl('funtest3',0,2,1,0.001);
t2=toc

t2 =

    0.2410

tic
[x1,y1]=rk_wjl('funtest3',0,2,1,0.001);
t1=toc

tic
[x2,y2]=adams_wjl('funtest3',0,2,1,0.001);
t2=toc

tic
[x1,y1]=rk_wjl('funtest3',0,2,1,0.001);
t1=toc

t1 =

    0.3110


tic
[x2,y2]=adams_wjl('funtest3',0,2,1,0.001);
t2=toc

t2 =

    0.2300

tic
[x1,y1]=rk_wjl('funtest3',0,2,1,0.001);
t1=toc

tic
[x2,y2]=adams_wjl('funtest3',0,2,1,0.001);
t2=toc
tic
[x1,y1]=rk_wjl('funtest3',0,2,1,0.001);
t1=toc

t1 =

    0.3210


tic
[x2,y2]=adams_wjl('funtest3',0,2,1,0.001);
t2=toc

t2 =

    0.2400

dbstack
;
disp(which('funtest2'));
e:\matlabtemp\funtest2.m
clear 'e:\matlabtemp\funtest2.m'
tic
[x1,y1]=rk_wjl('funtest2',0,2,1,0.001);
t1=toc

tic
[x2,y2]=adams_wjl('funtest2',0,2,1,0.001);
t2=toc
tic
[x1,y1]=rk_wjl('funtest2',0,2,1,0.001);
t1=toc

t1 =

    0.6310


tic
[x2,y2]=adams_wjl('funtest2',0,2,1,0.001);
t2=toc

t2 =

    0.2610

disp(which('funtest2'));
e:\matlabtemp\funtest2.m
clear 'e:\matlabtemp\funtest2.m'
tic
[x1,y1]=rk_wjl('funtest2',0,2,1,0.001);
t1=toc

tic
[x2,y2]=adams_wjl('funtest2',0,2,1,0.001);
t2=toc
tic
[x1,y1]=rk_wjl('funtest2',0,2,1,0.001);
t1=toc

t1 =

    0.3500


tic
[x2,y2]=adams_wjl('funtest2',0,2,1,0.001);
t2=toc

t2 =

    0.3110

tic
[x1,y1]=rk_wjl('funtest2',0,2,1,0.001);
t1=toc

tic
[x2,y2]=adams_wjl('funtest2',0,2,1,0.001);
t2=toc
tic
[x1,y1]=rk_wjl('funtest2',0,2,1,0.001);
t1=toc

t1 =

    0.3410


tic
[x2,y2]=adams_wjl('funtest2',0,2,1,0.001);
t2=toc

t2 =

    0.2700

tic
[x1,y1]=rk_wjl('funtest2',0,2,1,0.001);
t1=toc

tic
[x2,y2]=adams_wjl('funtest2',0,2,1,0.001);
t2=toc
tic
[x1,y1]=rk_wjl('funtest2',0,2,1,0.001);
t1=toc

t1 =

    0.3600


tic
[x2,y2]=adams_wjl('funtest2',0,2,1,0.001);
t2=toc

t2 =

    0.2400

tic
[x1,y1]=rk_wjl('funtest2',0,2,1,0.001);
t1=toc

tic
[x2,y2]=adams_wjl('funtest2',0,2,1,0.001);
t2=toc
tic
[x1,y1]=rk_wjl('funtest2',0,2,1,0.001);
t1=toc

t1 =

    0.3410


tic
[x2,y2]=adams_wjl('funtest2',0,2,1,0.001);
t2=toc

t2 =

    0.2800

tic
[x1,y1]=rk_wjl('funtest2',0,2,1,0.001);
t1=toc

tic
[x2,y2]=adams_wjl('funtest2',0,2,1,0.001);
t2=toc
tic
[x1,y1]=rk_wjl('funtest2',0,2,1,0.001);
t1=toc

t1 =

    0.4010


tic
[x2,y2]=adams_wjl('funtest2',0,2,1,0.001);
t2=toc

t2 =

    0.3000

tic
[x1,y1]=rk_wjl('funtest2',0,2,1,0.001);
t1=toc

tic
[x2,y2]=adams_wjl('funtest2',0,2,1,0.001);
t2=toc
tic
[x1,y1]=rk_wjl('funtest2',0,2,1,0.001);
t1=toc

t1 =

    0.3410


tic
[x2,y2]=adams_wjl('funtest2',0,2,1,0.001);
t2=toc

t2 =

    0.2900

tic
[x1,y1]=rk_wjl('funtest2',0,2,1,0.001);
t1=toc

tic
[x2,y2]=adams_wjl('funtest2',0,2,1,0.001);
t2=toc
tic
[x1,y1]=rk_wjl('funtest2',0,2,1,0.001);
t1=toc

t1 =

    0.3510


tic
[x2,y2]=adams_wjl('funtest2',0,2,1,0.001);
t2=toc

t2 =

    0.2900

dbstack
;
disp(which('na53test'));
e:\matlabtemp\na53test.m
clear 'e:\matlabtemp\na53test.m'
disp(which('na53test'));
e:\matlabtemp\na53test.m
clear 'e:\matlabtemp\na53test.m'
[x1,y1]=rk_wjl('funtest3',0,2,1,0.2);
[x2,y2]=adams_wjl('funtest3',0,2,1,0.2);
fprintf('%25.15f\n',y1(1:10))
fprintf('%25.15f\n',y2(1:10))
fprintf('%25.15f\n',x1(1:10))

[x1,y1]=rk_wjl('funtest3',0,2,1,0.2);
[x2,y2]=adams_wjl('funtest3',0,2,1,0.2);
fprintf('%25.15f\n',y1(1:10))
        1.000000000000000
        0.953809798603462
        0.803957187302435
        0.559930144914359
        0.258373645529882
       -0.048261190980325
       -0.303663865842853
       -0.458878611459712
       -0.481423834832514
       -0.361173917672502
fprintf('%25.15f\n',y2(1:10))
        1.000000000000000
        0.953809798603462
        0.803957187302435
        0.559930144914359
        0.257785374326456
       -0.049364325033627
       -0.305157070152266
       -0.460597093943443
       -0.483166716156006
       -0.362735165423133
fprintf('%25.15f\n',x1(1:10))
        0.000000000000000
        0.200000000000000
        0.400000000000000
        0.600000000000000
        0.800000000000000
        1.000000000000000
        1.200000000000000
        1.400000000000000
        1.600000000000000
        1.800000000000000
disp(which('na53test'));
e:\matlabtemp\na53test.m
clear 'e:\matlabtemp\na53test.m'

cc
[x1,y1]=rk_wjl('funtest3',0,2,1,0.2);
[x2,y2]=adams_wjl('funtest3',0,2,1,0.2);
[x1,y1]=rk_wjl('funtest3',0,2,1,0.2);
[x2,y2]=adams_wjl('funtest3',0,2,1,0.2);
dbstack
;
disp(which('exact52'));
e:\matlabtemp\exact52.m
mdbstatus 'e:\matlabtemp\exact52.m'
dbstack
;
disp(which('exact53'));
e:\matlabtemp\exact53.m
clear 'e:\matlabtemp\exact53.m'
[xe,ye]=evalf('exact53',x1);
[xe,ye]=evalf('exact53',x1);
??? Undefined function or variable 'evalf'.

disp(which('na53test'));
e:\matlabtemp\na53test.m
clear 'e:\matlabtemp\na53test.m'
[xe,ye]=feval('exact53',x1);
[xe,ye]=feval('exact53',x1);
??? Error using ==> exact53
Too many output arguments.

ye=feval('exact53',x1);
ye=feval('exact53',x1);
err1=abs(ye-y1);
err2=abs(ye-y2);
err1=abs(ye-y1);
err2=abs(ye-y2);
fprintf('%25.15f\n',y1(1:10))
fprintf('%25.15f\n',y2(1:10))
fprintf('%25.15f\n',x1(1:10))
fprintf('%25.15f\n',ye(1:10))
fprintf('%25.15f\n',y1(1:10))
        1.000000000000000
        0.953809798603462
        0.803957187302435
        0.559930144914359
        0.258373645529882
       -0.048261190980325
       -0.303663865842853