na53test.m

(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

%function na53test
[x1,y1]=rk_wjl('funtest3',0,2,1,0.1);
[x2,y2]=adams_wjl1('funtest3',0,2,1,0.1);
ye=feval('exact53',x1);
err1=y1-ye;
%err1=abs(y1-ye);
%err2=y2-ye;
err2=abs(y2-ye);
figure(1)
fprintf('%5.3f\n',x1(1:10))
fprintf('%+2.1e\n',err1(1:10))
fprintf('%+2.1e\n',err2(1:10))
plot(x1,err1,x1,err2)
legend('Runge-Kutta','Adams')
xlabel('x')
ylabel('y')
title('step=0.1,Error of problem3 with Runge-Kutta,Adams')


[x1,y1]=rk_wjl('funtest3',0,2,1,0.01);
[x2,y2]=adams_wjl1('funtest3',0,2,1,0.01);
ye=feval('exact53',x1);
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))

err1=y1-ye;
%err1=abs(y1-ye);
err2=y2-ye;
%err2=abs(y2-ye);
figure(2)
fprintf('%+2.1e\n',err1(1:10))
fprintf('%+2.1e\n',err2(1:10))
fprintf('%5.3f\n',x1(1:10))
plot(x1,err1,x1,err2)
legend('Runge-Kutta','Adams')
xlabel('x')
ylabel('y')
title('step=0.01,Error of problem3 with Runge-Kutta,Adams')

[x1,y1]=rk_wjl('funtest3',0,2,1,0.001);
[x2,y2]=adams_wjl1('funtest3',0,2,1,0.001);
ye=feval('exact53',x1);
err1=y1-ye;
%err1=abs(y1-ye);
%err2=y2-ye;
err2=abs(y2-ye);
figure(3)
fprintf('%+2.1e\n',err1(1:10))
fprintf('%+2.1e\n',err2(1:10))
fprintf('%5.3f\n',x1(1:10))
plot(x1,err1,x1,err2)
legend('Runge-Kutta','Adams')
xlabel('x')
ylabel('y')
title('step=0.001,Error of problem3 with Runge-Kutta,Adams')



[x1,y1]=rk_wjl('funtest3',0,30,1,0.1);
[x2,y2]=adams_wjl1('funtest3',0,30,1,0.1);
ye=feval('exact53',x1);
err1=y1-ye;
%err1=abs(y1-ye);
err2=y2-ye;
%err2=abs(y2-ye);
figure(4)
fprintf('%5.3f\n',x1(1:10))
fprintf('%+2.1e\n',err1(1:10))
fprintf('%+2.1e\n',err2(1:10))
plot(x1,err1,x1,err2)

legend('Runge-Kutta','Adams')
xlabel('x')
ylabel('y')
title('step=0.1,Range=0..30,Error of problem3 with Runge-Kutta,Adams')

figure(5)
plot(x1,y1,x2,y2,x1,ye)
legend('Runge-Kutta','Adams','exact')
xlabel('x')
ylabel('y')
title('step=0.1,Range=0..30,problem3 with Runge-Kutta,Adams')

[x1,y1]=rk_wjl('funtest3',0,30,1,0.01);
[x2,y2]=adams_wjl1('funtest3',0,30,1,0.01);
ye=feval('exact53',x1);
err1=y1-ye;
%err1=abs(y1-ye);
err2=y2-ye;
%err2=abs(y2-ye);
figure(6)
fprintf('%5.3f\n',x1(1:10))
fprintf('%+2.1e\n',err1(1:10))
fprintf('%+2.1e\n',err2(1:10))
plot(x1,err1,x1,err2)

legend('Runge-Kutta','Adams')
xlabel('x')
ylabel('y')
title('step=0.01,Range=0..30,Error of problem3 with Runge-Kutta,Adams')

figure(7)
plot(x1,y1,x2,y2,x1,ye)
legend('Runge-Kutta','Adams','exact')
xlabel('x')
ylabel('y')
title('step=0.01,Range=0..30,problem3 with Runge-Kutta,Adams')

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

tic;
[x2,y2]=adams_wjl1('funtest3',0,2,1,0.001);
t2=toc;
t1,t2