雅可比迭代法的
MA
TLAB
程序：
Function[x,k,index]=Jacobi(A,b,ep,it-max)
%
求线性方程组的雅可比法
;
% A
为方程组的系数矩阵
;
% b
为方程组的右端项
;
% x
为方程组的解
;
% ep
为精度要求
,
缺省值为
le-5;
% it_max
为最大迭代次数
,
缺省值为
100;
% k
为迭代次数
;
% index
为指标变量
,index=0
表示计算失败
,index=1
表示计算成功
;
if nargin<4
it_max=100;
end
if nargin<3
ep=le-5;
end
n=length(A);k=0;x=zeros(n,1);y=zeros(n,1);index=1;
while k<=it_max
for i=1:n
if abs (A(i,i))
index=0;
return;
end
y(i)=(b(i)-A(i,1:n)*x(1:n)+A(i,i)*x(i))/A(i,i);
end
if norm(y-x,inf)
break;
end
k=k+1;
x=y;
end
高斯
-
赛德尔迭代的
MATLAB
程序
Function[x,k,index]=Gau-seidel(A,b,ep,it-max)
%
求线性方程组的高斯
-
赛德尔迭代法
;
% A
为方程组的系数矩阵
;
% b
为方程组的右端项
;
% x
为方程组的解
;
% ep
为精度要求
,
缺省值为
le-5;
% it_max
为最大迭代次数
,
缺省值为
100;
% k
为迭代次数
;
% index
为指标变量
,index=0
表示计算失败
,index=1
表示计算成功
;
if nargin<4
it_max=100;

/*简单牛顿迭代法的MATLAB程序实现*/
function x=newtoniteration(fun,dfun,x0,EPS) %简单牛顿迭代法
%fun即迭代函数，dfun即迭代函数的一阶导数，x0为迭代初值，EPS为精度
f=fcnchk(fun);
df=fcnchk(fun);
x1=x0-f(x0)/df(x0);
d=norm(x1-x0);
k=1;
while d>=EPS
	x0=x1;
	x1=x0-f(x0)/df(x0);
	d=norm(x1-x0);
	k=k+1;
end
x=x1; %切记要给x赋值

/*简单牛顿迭代法的MATLAB程序实现2，增加了迭代次数的限制*/
function x=newtoniteration(fun,dfun,x0,EPS) %简单牛顿迭代法
%fun即迭代函数，dfun即迭代函数的一阶导数，x0为迭代初值，EPS为精度
f=fcnchk(fun);
df=fcnchk(fun);
x1=x0-df(x0)\f(x0); %左除
d=norm(x1-x0);
k=1;
while d>=EPS
	x0=x1;
	x1=x0-df(x0)\f(x0); %左除
	d=norm(x1-x0);
	k=k+1;
end
if k==1000
	x='fasan';
else
	x=x1;
end

友情链接们：

（1）MATLAB 牛顿迭代法解非线性方程组

https://blog.csdn.net/mlp750303040/article/details/77479654牛顿迭代法的MATLAB程序
（2）牛顿迭代法求方程根的matlab程序http://blog.sina.com.cn/s/blog_6faf74c00101cr9d.html
（3）牛顿迭代法求方程根的MATLAB程序

https://blog.51cto.com/592669550/930491
（4）MATLAB 单变量函数一阶及N阶求导

https://www.cnblogs.com/shuqingstudy/p/4844952.html
（5）牛顿迭代法的MATLAB程序

https://wenku.baidu.com/view/a606ce9ddd3383c4bb4cd292.html

二维时间隐式格式点迭代MATLAB程序
代码改编自二维时间隐式格式点迭代C程序

下面是代码
%iteration implicit time 2d
clc
clear
%%
LengthX = 3;
LengthY = 2;
Tleft = 3.5;
Tright = 5;
Tbottom = 2;
Tup = 4;
den = 100;
s = 10;
k=10;
cv = 1000;
%%
dt = 200;
N = 15;%X
M = 15;%Y
maxstep = 200;
itermax = 1000;
maxresi = 1e-7;
%%
dx =LengthX/N;
dy =LengthY/M;
ae1 = zeros(M+2,N+2);
aw1 = zeros(M+2,N+2);
an1 = zeros(M+2,N+2);
as1 = zeros(M+2,N+2);
ap0 = zeros(M+2,N+2);
ap1 = zeros(M+2,N+2);
b= zeros(M+2,N+2);
T0 =zeros(M+2,N+2);
T1 = zeros(M+2,N+2);

resi = zeros(M+2,N+2);
Tall = zeros(M+2,maxstep+1);
resiall = zeros(maxstep,1);
iterall = zeros(maxstep,1);
%% 边界条件
T0(2:M+1,2:N+1) = 3;
T0(1:M+2,1) = Tleft;
T0(1:M+2,N+2) = Tright;
T0(1,1:N+2) = Tup;
T0(M+2,1:N+2) = Tbottom;

T1(1:M+2,1) = Tleft;
T1(1:M+2,N+2) = Tright;
T1(1,1:N+2) = Tup;
T1(M+2,1:N+2) = Tbottom;
%% 网格系数计算
%内部网格计算
%% 网格系数计算
%内部网格计算
ae1(3:M,3:N) = k*dy/dx;
aw1(3:M,3:N) = k*dy/dx;
an1(3:M,3:N) = k*dx/dy;
as1(3:M,3:N) = k*dx/dy;
ap0(3:M,3:N) = den*cv*dx*dy/dt;
ap1(3:M,3:N) = ap0(3:M,3:N)+ae1(3:M,3:N)+aw1(3:M,3:N)+an1(3:M,3:N)+as1(3:M,3:N);
b(3:M,3:N) = s*dx*dy;
%边界网格计算
%第一个
i=2;
for j=3:N
    ae1(i,j) = k*dy/dx;
    aw1(i,j) = k*dy/dx;
    an1(i,j) = k*dx/(dy/2);
    as1(i,j) = k*dx/dy;
    ap0(i,j) = den*cv*dx*dy/dt;
    ap1(i,j) = ap0(i,j)+ae1(i,j)+aw1(i,j)+an1(i,j)+as1(i,j);
    b(i,j) = s*dx*dy;
end

i=M+1;
for j=3:N
    ae1(i,j) = k*dy/dx;
    aw1(i,j) = k*dy/dx;
    an1(i,j) = k*dx/dy;
    as1(i,j) = k*dx/(dy/2);
    ap0(i,j) = den*cv*dx*dy/dt;
    ap1(i,j) = ap0(i,j)+ae1(i,j)+aw1(i,j)+an1(i,j)+as1(i,j);
    b(i,j) = s*dx*dy;
end
j=2;
for i=3:M
    ae1(i,j) = k*dy/dx;
    aw1(i,j) = k*dy/(dx/2);
    an1(i,j) = k*dx/dy;
    as1(i,j) = k*dx/dy;
    ap0(i,j) = den*cv*dx*dy/dt;
    ap1(i,j) = ap0(i,j)+ae1(i,j)+aw1(i,j)+an1(i,j)+as1(i,j);
    b(i,j) = s*dx*dy;
end
j=N+1;
for i=3:M
    ae1(i,j) = k*dy/(dx/2);
    aw1(i,j) = k*dy/dx;
    an1(i,j) = k*dx/dy;
    as1(i,j) = k*dx/dy;
    ap0(i,j) = den*cv*dx*dy/dt;
    ap1(i,j) = ap0(i,j)+ae1(i,j)+aw1(i,j)+an1(i,j)+as1(i,j);
    b(i,j) = s*dx*dy;
end

j=2;
i=2;
ae1(i,j) = k*dy/dx;
aw1(i,j) = k*dy/(dx/2);
an1(i,j) = k*dx/(dy/2);
as1(i,j) = k*dx/dy;
ap0(i,j) = den*cv*dx*dy/dt;
ap1(i,j) = ap0(i,j)+ae1(i,j)+aw1(i,j)+an1(i,j)+as1(i,j);
b(i,j) = s*dx*dy;

j=2;
i=M+1;
ae1(i,j) = k*dy/dx;
aw1(i,j) = k*dy/(dx/2);
an1(i,j) = k*dx/dy;
as1(i,j) = k*dx/(dy/2);
ap0(i,j) = den*cv*dx*dy/dt;
ap1(i,j) = ap0(i,j)+ae1(i,j)+aw1(i,j)+an1(i,j)+as1(i,j);
b(i,j) = s*dx*dy;

i=2;
j=N+1;
ae1(i,j) = k*dy/(dx/2);
aw1(i,j) = k*dy/dx;
an1(i,j) = k*dx/(dy/2);
as1(i,j) = k*dx/dy;
ap0(i,j) = den*cv*dx*dy/dt;
ap1(i,j) = ap0(i,j)+ae1(i,j)+aw1(i,j)+an1(i,j)+as1(i,j);
b(i,j) = s*dx*dy;

i=M+1;
j=N+1;
ae1(i,j) = k*dy/(dx/2);
aw1(i,j) = k*dy/dx;
an1(i,j) = k*dx/dy;
as1(i,j) = k*dx/(dy/2);
ap0(i,j) = den*cv*dx*dy/dt;
ap1(i,j) = ap0(i,j)+ae1(i,j)+aw1(i,j)+an1(i,j)+as1(i,j);
b(i,j) = s*dx*dy;
%%
Tall(1:M+2,1:N+2) = T0;
%% iteration
for h = 1:maxstep
    Tn0 = T0;
    for iter = 1:itermax
        for i=M+1:-1:2
            for j=2:N+1
                T1(i,j) = (ae1(i,j)*Tn0(i,j+1)+aw1(i,j)*Tn0(i,j-1)...
                    +an1(i,j)*Tn0(i-1,j)+as1(i,j)*Tn0(i+1,j)...
                    +ap0(i,j)*T0(i,j)+b(i,j))/ap1(i,j);
            end
        end
        resimax = max(max(abs(T1-Tn0)));
        if resimax<maxresi
            break;
        end
        Tn0 = T1;
    end
    resiall(h) = resimax;
    iterall(h) = iter;
    T0=T1;
    Tall((h)*(M+2)+1:(h+1)*(M+2),1:N+2) = T0;
end
T11=zeros(maxstep,1);
for i =1:maxstep+1
    T11(i) = Tall((i-1)*(M+2)+2,2);%选取网格观察温度变化
end
plot(dt:dt:dt*maxstep,T11(2:maxstep+1));
hold on