📄 sy15.mht
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pt'><span
lang=3DEN-US>y0</span><span style=3D'font-family:SimSun;mso-ascii-font-fami=
ly:"Times New Roman";
mso-hansi-font-family:"Times New Roman"'>初始条件&#=
12290;</span></p>
<p class=3DMsoNormal align=3Dleft style=3D'text-align:left;text-indent:21.0=
pt'><span
style=3D'font-family:SimSun;mso-ascii-font-family:"Times New Roman";mso-han=
si-font-family:
"Times New Roman"'>例</span><span lang=3DEN-US>5</span><span
style=3D'font-family:SimSun;mso-ascii-font-family:"Times New Roman";mso-han=
si-font-family:
"Times New Roman"'>:求解微分方程=
</span><span
lang=3DEN-US><sub><!--[if gte vml 1]><v:shape id=3D"_x0000_i1038" type=3D"#=
_x0000_t75"
style=3D'width:96.75pt;height:18pt' o:ole=3D"">
<v:imagedata src=3D"sy15.files/image023.wmz" o:title=3D""/>
</v:shape><![endif]--><![if !vml]><img width=3D129 height=3D24
src=3D"sy15.files/image024.gif" v:shapes=3D"_x0000_i1038"><![endif]></sub><=
!--[if gte mso 9]><xml>
<o:OLEObject Type=3D"Embed" ProgID=3D"Equation.DSMT4" ShapeID=3D"_x0000_i1=
038"
DrawAspect=3D"Content" ObjectID=3D"_1237614482">
</o:OLEObject>
</xml><![endif]--></span><span style=3D'font-family:SimSun;mso-ascii-font-f=
amily:
"Times New Roman";mso-hansi-font-family:"Times New Roman"'>,</span><=
span
lang=3DEN-US><sub><!--[if gte vml 1]><v:shape id=3D"_x0000_i1039" type=3D"#=
_x0000_t75"
style=3D'width:54pt;height:14.25pt' o:ole=3D"">
<v:imagedata src=3D"sy15.files/image025.wmz" o:title=3D""/>
</v:shape><![endif]--><![if !vml]><img width=3D72 height=3D19
src=3D"sy15.files/image026.gif" v:shapes=3D"_x0000_i1039"><![endif]></sub><=
!--[if gte mso 9]><xml>
<o:OLEObject Type=3D"Embed" ProgID=3D"Equation.DSMT4" ShapeID=3D"_x0000_i1=
039"
DrawAspect=3D"Content" ObjectID=3D"_1237614483">
</o:OLEObject>
</xml><![endif]--></span><span style=3D'font-family:SimSun;mso-ascii-font-f=
amily:
"Times New Roman";mso-hansi-font-family:"Times New Roman"'>,</span><=
span
lang=3DEN-US><sub><!--[if gte vml 1]><v:shape id=3D"_x0000_i1040" type=3D"#=
_x0000_t75"
style=3D'width:41.25pt;height:15.75pt' o:ole=3D"">
<v:imagedata src=3D"sy15.files/image027.wmz" o:title=3D""/>
</v:shape><![endif]--><![if !vml]><img width=3D55 height=3D21
src=3D"sy15.files/image028.gif" v:shapes=3D"_x0000_i1040"><![endif]></sub><=
!--[if gte mso 9]><xml>
<o:OLEObject Type=3D"Embed" ProgID=3D"Equation.DSMT4" ShapeID=3D"_x0000_i1=
040"
DrawAspect=3D"Content" ObjectID=3D"_1237614484">
</o:OLEObject>
</xml><![endif]--></span><span style=3D'font-family:SimSun;mso-ascii-font-f=
amily:
"Times New Roman";mso-hansi-font-family:"Times New Roman"'>的</span><=
span
lang=3DEN-US>MATLAB</span><span style=3D'font-family:SimSun;mso-ascii-font-=
family:
"Times New Roman";mso-hansi-font-family:"Times New Roman"'>程序=
如下:</span><span
lang=3DEN-US>fun=3Dinline('-2*y+2*x*x+2*x')</span><span style=3D'font-famil=
y:SimSun;
mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Times New Ro=
man"'>;</span><span
lang=3DEN-US>[<span class=3DSpellE><span class=3DGramE>x,</span>y</span>]=
=3D<span
class=3DGramE>ode23(</span>fun,[0,0.5],1)</span></p>
<p class=3DMsoNormal align=3Dleft style=3D'text-align:left'><span style=3D'=
font-family:
SimSun;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Times=
New Roman"'>结果为:</span></p>
<p class=3DMsoNormal align=3Dleft style=3D'text-align:left'><span lang=3DEN=
-US>x =3D
0,0.0400,0.0900,0.1400,0.1900,0.2400,0.2900,0.3400,0.3900,0.4400,0.4900,0.5=
000</span></p>
<p class=3DMsoNormal align=3Dleft style=3D'text-align:left'><span lang=3DEN=
-US>y =3D
1.0000,0.9247,0.8434,0.7754,0.7199,0.6764,0.6440,0.6222,0.6105,0.6084,0.615=
4,0.6179</span></p>
<p class=3DMsoNormal align=3Dleft style=3D'text-align:left;text-indent:21.0=
pt'><span
style=3D'font-family:SimSun;mso-ascii-font-family:"Times New Roman";mso-han=
si-font-family:
"Times New Roman"'>例</span><span lang=3DEN-US>6</span><span
style=3D'font-family:SimSun;mso-ascii-font-family:"Times New Roman";mso-han=
si-font-family:
"Times New Roman"'>:求解微分方程=
</span><span
lang=3DEN-US><sub><!--[if gte vml 1]><v:shape id=3D"_x0000_i1041" type=3D"#=
_x0000_t75"
style=3D'width:218.25pt;height:33pt' o:ole=3D"">
<v:imagedata src=3D"sy15.files/image029.wmz" o:title=3D""/>
</v:shape><![endif]--><![if !vml]><img width=3D291 height=3D44
src=3D"sy15.files/image030.gif" v:shapes=3D"_x0000_i1041"><![endif]></sub><=
!--[if gte mso 9]><xml>
<o:OLEObject Type=3D"Embed" ProgID=3D"Equation.DSMT4" ShapeID=3D"_x0000_i1=
041"
DrawAspect=3D"Content" ObjectID=3D"_1237614485">
</o:OLEObject>
</xml><![endif]--></span><span style=3D'font-family:SimSun;mso-ascii-font-f=
amily:
"Times New Roman";mso-hansi-font-family:"Times New Roman"'>的解=
,并画出解的图形。</s=
pan></p>
<p class=3DMsoNormal align=3Dleft style=3D'text-align:left;text-indent:21.0=
pt'><span
style=3D'font-family:SimSun;mso-ascii-font-family:"Times New Roman";mso-han=
si-font-family:
"Times New Roman"'>分析:这是一个=
二阶非线性方程,用=
9616;成的方法均不能求෉=
9;,但我们可以通过下&=
#38754;的变换,将二阶方=
243;化为一阶方程组,即=
;可求解。</span></p>
<p class=3DMsoNormal align=3Dleft style=3D'text-align:left;text-indent:21.0=
pt'><span
style=3D'font-family:SimSun;mso-ascii-font-family:"Times New Roman";mso-han=
si-font-family:
"Times New Roman"'>令:</span><span lang=3DEN-US><sub><!--[if g=
te vml 1]><v:shape
id=3D"_x0000_i1042" type=3D"#_x0000_t75" style=3D'width:32.25pt;height:18p=
t' o:ole=3D"">
<v:imagedata src=3D"sy15.files/image031.wmz" o:title=3D""/>
</v:shape><![endif]--><![if !vml]><img width=3D43 height=3D24
src=3D"sy15.files/image032.gif" v:shapes=3D"_x0000_i1042"><![endif]></sub><=
!--[if gte mso 9]><xml>
<o:OLEObject Type=3D"Embed" ProgID=3D"Equation.DSMT4" ShapeID=3D"_x0000_i1=
042"
DrawAspect=3D"Content" ObjectID=3D"_1237614486">
</o:OLEObject>
</xml><![endif]--></span><span style=3D'font-family:SimSun;mso-ascii-font-f=
amily:
"Times New Roman";mso-hansi-font-family:"Times New Roman"'>,</span><=
span
lang=3DEN-US><sub><!--[if gte vml 1]><v:shape id=3D"_x0000_i1043" type=3D"#=
_x0000_t75"
style=3D'width:39.75pt;height:30.75pt' o:ole=3D"">
<v:imagedata src=3D"sy15.files/image033.wmz" o:title=3D""/>
</v:shape><![endif]--><![if !vml]><img width=3D53 height=3D41
src=3D"sy15.files/image034.gif" v:shapes=3D"_x0000_i1043"><![endif]></sub><=
!--[if gte mso 9]><xml>
<o:OLEObject Type=3D"Embed" ProgID=3D"Equation.DSMT4" ShapeID=3D"_x0000_i1=
043"
DrawAspect=3D"Content" ObjectID=3D"_1237614487">
</o:OLEObject>
</xml><![endif]--></span><span style=3D'font-family:SimSun;mso-ascii-font-f=
amily:
"Times New Roman";mso-hansi-font-family:"Times New Roman"'>,</span><=
span
lang=3DEN-US><sub><!--[if gte vml 1]><v:shape id=3D"_x0000_i1044" type=3D"#=
_x0000_t75"
style=3D'width:30pt;height:15.75pt' o:ole=3D"">
<v:imagedata src=3D"sy15.files/image035.wmz" o:title=3D""/>
</v:shape><![endif]--><![if !vml]><img width=3D40 height=3D21
src=3D"sy15.files/image036.gif" v:shapes=3D"_x0000_i1044"><![endif]></sub><=
!--[if gte mso 9]><xml>
<o:OLEObject Type=3D"Embed" ProgID=3D"Equation.DSMT4" ShapeID=3D"_x0000_i1=
044"
DrawAspect=3D"Content" ObjectID=3D"_1237614488">
</o:OLEObject>
</xml><![endif]--></span><span style=3D'font-family:SimSun;mso-ascii-font-f=
amily:
"Times New Roman";mso-hansi-font-family:"Times New Roman"'>,则=
得到:</span></p>
<p class=3DMsoNormal align=3Dleft style=3D'text-align:left;text-indent:21.0=
pt'><span
lang=3DEN-US><sub><!--[if gte vml 1]><v:shape id=3D"_x0000_i1045" type=3D"#=
_x0000_t75"
style=3D'width:167.25pt;height:66pt' o:ole=3D"">
<v:imagedata src=3D"sy15.files/image037.wmz" o:title=3D""/>
</v:shape><![endif]--><![if !vml]><img width=3D223 height=3D88
src=3D"sy15.files/image038.gif" v:shapes=3D"_x0000_i1045"><![endif]></sub><=
!--[if gte mso 9]><xml>
<o:OLEObject Type=3D"Embed" ProgID=3D"Equation.DSMT4" ShapeID=3D"_x0000_i1=
045"
DrawAspect=3D"Content" ObjectID=3D"_1237614489">
</o:OLEObject>
</xml><![endif]--></span></p>
<p class=3DMsoNormal align=3Dleft style=3D'text-align:left'><!--[if gte vml=
1]><v:shape
id=3D"_x0000_s1026" type=3D"#_x0000_t75" style=3D'position:absolute;margin=
-left:0;
margin-top:1.8pt;width:223.5pt;height:168pt;z-index:1;
mso-position-horizontal:left'>
<v:imagedata src=3D"sy15.files/image039.png" o:title=3D""/>
<w:wrap type=3D"square"/>
</v:shape><![endif]--><![if !vml]><img width=3D298 height=3D224
src=3D"sy15.files/image040.jpg" align=3Dleft hspace=3D12 v:shapes=3D"_x0000=
_s1026"><![endif]><span
style=3D'font-family:SimSun;mso-ascii-font-family:"Times New Roman";mso-han=
si-font-family:
"Times New Roman"'>接着,编写</span><span
class=3DSpellE><span lang=3DEN-US>vdp.m</span></span><span style=3D'font-fa=
mily:SimSun;
mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Times New Ro=
man"'>如下:</span></p>
<p class=3DMsoNormal align=3Dleft style=3D'text-align:left'><span class=3DG=
ramE><span
lang=3DEN-US>function</span></span><span lang=3DEN-US> <span class=3DSpellE=
>fy</span>=3D<span
class=3DSpellE>vdp</span>(<span class=3DSpellE>t,x</span>)</span></p>
<p class=3DMsoNormal align=3Dleft style=3D'text-align:left'><span class=3DS=
pellE><span
class=3DGramE><span lang=3DEN-US>fy</span></span></span><span lang=3DEN-US>=
=3D[x(2);7*(1-x(1)^2)*x(2)-x(1)];</span></p>
<p class=3DMsoNormal align=3Dleft style=3D'text-align:left'><span style=3D'=
font-family:
SimSun;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Times=
New Roman"'>再编写</span><span
lang=3DEN-US>m</span><span style=3D'font-family:SimSun;mso-ascii-font-famil=
y:"Times New Roman";
mso-hansi-font-family:"Times New Roman"'>文件</span><span
lang=3DEN-US>sy7_6.m</span><span style=3D'font-family:SimSun;mso-ascii-font=
-family:
"Times New Roman";mso-hansi-font-family:"Times New Roman"'>如下=
:</span></p>
<p class=3DMsoNormal align=3Dleft style=3D'text-align:left'><span lang=3DEN=
-US>y0<span
class=3DGramE>=3D[</span>1;0]</span></p>
<p class=3DMsoNormal align=3Dleft style=3D'text-align:left'><span lang=3DEN=
-US>[<span
class=3DSpellE><span class=3DGramE>t,</span>x</span>]=3D<span class=3DGramE=
>ode45(</span>@<span
class=3DSpellE>vdp</span>,[0,40],y0);</span></p>
<p class=3DMsoNormal align=3Dleft style=3D'text-align:left'><span lang=3DES
style=3D'mso-ansi-language:ES'>y=3Dx(:,1);dy=3Dx(:,2);<o:p></o:p></span></p>
<p class=3DMsoNormal align=3Dleft style=3D'text-align:left'><span lang=3DES
style=3D'mso-ansi-language:ES'>plot(t,y,t,dy)<o:p></o:p></span></p>
<p class=3DMsoNormal align=3Dleft style=3D'text-align:left'><span lang=3DES
style=3D'mso-ansi-language:ES'><o:p> </o:p></span></p>
<p class=3DMsoNormal align=3Dleft style=3D'text-align:left'><span lang=3DES
style=3D'mso-ansi-language:ES'><o:p> </o:p></span></p>
<p class=3DMsoNormal align=3Dleft style=3D'text-align:left'><b style=3D'mso=
-bidi-font-weight:
normal'><span lang=3DES style=3D'mso-ansi-language:ES'><o:p> </o:p></s=
pan></b></p>
<p class=3DMsoNormal align=3Dleft style=3D'text-align:left'><b style=3D'mso=
-bidi-font-weight:
normal'><span style=3D'font-family:SimSun;mso-ascii-font-family:"Times New =
Roman";
mso-hansi-font-family:"Times New Roman"'>三、实验&#=
20869;容</span><span
lang=3DEN-US><o:p></o:p></span></b></p>
<p class=3DMsoNormal align=3Dleft style=3D'text-align:left'><span lang=3DEN=
-US>1</span><span
style=3D'font-family:SimSun;mso-ascii-font-family:"Times New Roman";mso-han=
si-font-family:
"Times New Roman"'>.利用</span><span lang=3DEN-US>MATLAB=
</span><span
style=3D'font-family:SimSun;mso-ascii-font-family:"Times New Roman";mso-han=
si-font-family:
"Times New Roman"'>求常微分方程的=
初值问题</span><span
lang=3DEN-US><sub><!--[if gte vml 1]><v:shape id=3D"_x0000_i1046" type=3D"#=
_x0000_t75"
style=3D'width:57.75pt;height:30.75pt' o:ole=3D"">
<v:imagedata src=3D"sy15.files/image041.wmz" o:title=3D""/>
</v:shape><![endif]--><![if !vml]><img width=3D77 height=3D41
src=3D"sy15.files/image042.gif" v:shapes=3D"_x0000_i1046"><![endif]></sub><=
!--[if gte mso 9]><xml>
<o:OLEObject Type=3D"Embed" ProgID=3D"Equation.DSMT4" ShapeID=3D"_x0000_i1=
046"
DrawAspect=3D"Content" ObjectID=3D"_1237614490">
</o:OLEObject>
</xml><![endif]--></span><span style=3D'fon
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