euler方法以及euler改进

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1、Euler方法以及Euler改进方法的主程序：formatlongfun='x+y';a=-0.2;b=0.2;h=0.02;n=(b-a)/h;X=a:h:b;Y=zeros(1,n+1);X(1)=a;Y1(1)=1;Y2(1)=1;Y3(1)=1;%Euler方法fori=1:nx=X(i);y=Y1(i);Y1(i+1)=Y1(i)+h*eval(fun);end%Euler预测-校正方法X(1)=a;Y2(1)=1;fori=1:nx=X(i);y=Y2(i);YP=Y2(i)+h*eval(fun);YC=Y2(i)+h*eval(fun);Y2(i+1)=

2、(YP+YC)/2end%计算精确值fun1='2*exp(x)-x-1';fori=1:nx=X(i+1);Y3(i+1)=eval(fun1)end[X',Y1',Y2',Y3']%显示结果%绘制结果图形fplot(fun1,[a,b])holdonplot(X,Y1,'*r',X,Y2,'+m')holdonplot(X,Y3,'ok')title('a,b取值为[-0.2，0.2]')return当a，b取不同的值的时候：[0,0.1]ans=01.0000000000000001.0000000000000001.0000000000000000.020000

3、0000000001.0200000000000001.0204000000000001.0204026800535120.0400000000000001.0408000000000001.0416160800000001.0416215483847760.0600000000000001.0624160000000001.0636647248160001.0636730930907190.0800000000000001.0848643200000001.0865627522572831.0865741353499170.1000000000000001.10816

4、16064000001.1103273198528801.110341836151295[-0.1,0.1]ans=-0.1000000000000001.0000000000000001.0000000000000001.000000000000000-0.0800000000000001.0180000000000001.0183800000000000.926232692773272-0.0600000000000001.0367600000000001.0375352760000000.943529067168497-0.0400000000000001.056

5、2952000000001.0574814885752000.961578878304646-0.0200000000000001.0766211040000001.0782346146444200.98039734661351101.0977535260800001.0998109538602371.0000000000000000.0200000000000001.1197085966016001.1222271351282141.0204026800535120.0400000000000001.1425027685336321.1455001232578041.

6、0416215483847760.0600000000000001.1661528239043051.1696472257476111.0636730930907190.0800000000000001.1906758803823911.1946860997077131.0865741353499170.1000000000000001.2160893979900391.2206347589218091.110341836151295[0,0.2]ans=01.0000000000000001.0000000000000001.0000000000000000.0200

7、000000000001.0200000000000001.0204000000000001.0204026800535120.0400000000000001.0408000000000001.0416160800000001.0416215483847760.0600000000000001.0624160000000001.0636647248160001.0636730930907190.0800000000000001.0848643200000001.0865627522572831.0865741353499170.1000