(第一边界条件源代码:
function y=yt1(x0,y0,f_0,f_n,x _____________(1 %第一类边界条件下三次样条插值;
%xi 所求点;
%yi所求点函数值;
%x 已知插值点;
%y 已知插值点函数值;
%f_0左端点一次导数值;
%f_n右端点一次导数值;
n = length(x0;
z = length(y0;
h = zeros(n-1,1;
k=zeros(n-2,1;
l=zeros(n-2,1;
S=2*eye(n;
fori=1:n-1
h(i= x0(i+1-x0(i;
end
fori=1:n-2
k(i= h(i+1/(h(i+1+h(i;
l(i= 1-k(i;
end
%对于第一种边界条件:
k = [1;k]; _______________________(2 l = [l;1]; _______________________(3 %构建系数矩阵 S :
fori = 1:n-1
S(i,i+1 = k(i;
S(i+1,i = l(i;
end
%建立均差表:
F=zeros(n-1,2;
fori = 1:n-1
F(i,1 = (y0(i+1-y0(i/(x0(i+1-x0(i;
end
D = zeros(n-2,1;
fori = 1:n-2
F(i,2 = (F(i+1,1-F(i,1/(x0(i+2-x0(i;
D(i,1 = 6 * F(i,2;
end
%构建函数 D :
d0 = 6*(F(1,2-f_0/h(1; ___________(4
dn = 6*(f_n-F(n-1,2/h(n-1; ___________(5
D = [d0;D;dn]; ______________(6
m= S\D;
%寻找 x 所在位置,并求出对应插值:
fori = 1:length(x
for j = 1:n-1
if (x(i<=x0(j+1&(x(i>=x0(j
y(i =( m(j*(x0(j+1-x(i^3/(6*h(j+...
(m(j+1*(x(i-x0(j^3/(6*h(j+...
(y0(j-(m(j*h(j^2/6*(x0(j+1-x(i/h(j+... (y0(j+1-(m(j+1*h(j^2/6*(x(i-x0(j/h(j ; break; else continue;
end
end
end
(2 (自然边界条件源代码:
仅仅需要对上面部分标注的位置做如下修改 :
__(1:function y=yt2(x0,y0,x __(2:k=[0;k]
__(3:l=[l;0]
__(4+(5:删除
— (6:D=[0:D:0]
