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1、实用文档偏微分方程数值解实验报告文案大全实用文档一、题目：1、用有限元方法求下列边值问题的数值解：其中其精确解为，取h=0.1要求：（1）将精确解与用有限元得到的数值解画在同一图中（2）、、2、用线性元求解下列问题的数值解：精确到小数点后第六位，并画出解曲面。文案大全实用文档2、用Crank-Nicolson差分法求解Burger方程其中取要求画出解曲面。迭代格式如下：二、代码：1、%RitzGalerkin方法求解方程functionu1=Ritz(x)%定义步长h=1/100;x=0:h:1;n
2、=1/h;a=zeros(n-1,1);b=zeros(n,1);c=zeros(n-1,1);d=zeros(n,1);%求解Ritz方法中内点系数矩阵fori=1:1:n-1b(i)=(1/h+h*pi*pi/12)*2;文案大全实用文档d(i)=h*pi*pi/2*sin(pi/2*(x(i)+h))/2+h*pi*pi/2*sin(pi/2*x(i+1))/2;end%右侧导数条件边界点的计算b(n)=(1/h+h*pi*pi/12);d(n)=h*pi*pi/2*sin(pi/2*(x(i
3、)+h))/2;fori=1:1:n-1a(i)=-1/h+h*pi*pi/24;c(i)=-1/h+h*pi*pi/24;end%调用追赶法u=yy(a,b,c,d)%得到数值解向量u1=[0,u]%对分段区间做图plot(x,u1)%得到解析解y1=sin(pi/2*x);holdonplot(x,y1,'o')legend('数值解','解析解')functionx=yy(a,b,c,d)n=length(b);q=zeros(n,1);p=zeros(n,1);q(1)=b(1);p(1)=
4、d(1);fori=2:1:nq(i)=b(i)-a(i-1)*c(i-1)/q(i-1);文案大全实用文档p(i)=d(i)-p(i-1)*c(i-1)/q(i-1);endx(n)=p(n)/q(n);forj=n-1:-1:1x(j)=(p(j)-a(j)*x(j+1))/q(j);endxx=Columns1through110.01570.03140.04710.06280.07850.09410.10970.12530.14090.15640.1719Columns12through22
5、文案大全实用文档0.18740.20280.21810.23350.24870.26390.27900.29400.30900.32390.3387Columns23through330.35350.36810.38270.39720.41150.42580.44000.45400.46790.48180.4955Columns34through440.50910.52250.53580.54900.56210.57500.58780.60040.61290.62530.6374Columns45t
6、hrough550.64950.66130.67300.68460.69590.70710.71810.72900.73970.75010.7604Columns56through660.77050.78050.79020.79970.80900.81820.82710.83580.84440.85270.8608Columns67through770.86870.87630.88380.89100.89810.90490.91140.91780.92390.92980.9355Columns78t
7、hrough88文案大全实用文档0.94090.94610.95110.95580.96030.96460.96860.97240.97590.97930.9823Columns89through990.98510.98770.99010.99210.99400.99560.99690.99810.99890.99950.9999Column1001.0000u=Columns1through110.01570.03140.04710.06280.07850.09410.10970.12530.14
8、090.15640.1719Columns12through220.18740.20280.21810.23350.24870.26390.27900.29400.30900.32390.3387Columns23through330.35350.36810.38270.39720.41150.42580.44000.45400.46790.48180.4955文案大全实用文档Columns34through440.50910.52250.53580.54900.56
