# This cell in Sage mode
var('u')
H0 = (1-u)^2*(1+2*u)
H1 = (1-u)^2*u
H2 = (u-1)*u^2
H3 = (3-2*u)*u^2
G = plot(H0,(u,0,1),color='black')+plot(H1,(u,0,1),color='red')+plot(H2,(u,0,1),color='green')+plot(H3,(u,0,1),color='blue')
show(G,aspect_ratio=1)
|
The rest of this is in octave mode
function y = H0(u)
y = (1-u) .^2 .* (1+2*u)
end
function y = H1(u)
y = (1-u) .^2 .*u
end
function y = H2(u)
y = (u-1) .* u .^2
end
function y = H3(u)
y = (3-2 .*u) .* u .^2
end
n = 3
x = [-1 2 3 7]
y = [5 4 2 3]
m = [1 -2 1 -1]
for k = 2:n+1
xx = x(k-1):0.5:x(k);
delx = x(k)-x(k-1);
yy = H0( (xx-x(k-1))/(x(k)-x(k-1)) )*y(k-1) + H1( (xx-x(k-1))/(x(k)-x(k-1)) )*m(k-1)*delx + H2( (xx-x(k-1))/(x(k)-x(k-1)) )*m(k)*delx + H3( (xx-x(k-1))/(x(k)-x(k-1)) )*y(k);
plot(xx,yy)
hold on
end
n = 3
x =
-1 2 3 7
y =
5 4 2 3
m =
1 -2 1 -1
y =
1 0.925926 0.740741 0.5 0.259259 0.0740741 0
y =
0 0.115741 0.148148 0.125 0.0740741 0.0231481 0
y =
-0 -0.0231481 -0.0740741 -0.125 -0.148148 -0.115741 0
y =
0 0.0740741 0.259259 0.5 0.740741 0.925926 1
y =
1 0.5 0
y =
0 0.125 0
y =
-0 -0.125 0
y =
0 0.5 1
y =
1 0.957031 0.84375 0.683594 0.5 0.316406 0.15625 0.0429688 0
y =
0 0.0957031 0.140625 0.146484 0.125 0.0878906 0.046875 0.0136719 0
y =
-0 -0.0136719 -0.046875 -0.0878906 -0.125 -0.146484 -0.140625
-0.0957031 0
y =
0 0.0429688 0.15625 0.316406 0.5 0.683594 0.84375 0.957031 1
6
|-----------------------------------------------------------------------\
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| *********
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| *** *
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| ** *
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5 |-+ * *
+-|
| *
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| *
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| *
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| *
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4 |-+ #
+-|
| #
|
| # $$$$$$$$$$$
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| # $$ $$$
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| # $$$ $
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3 |-+ # $$ $
+-|
| # $
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| ## $
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| ## $$
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| + + $$ + +
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2
|-----------------------------------------------------------------------\
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-2 0 2 4 6
8
n = 3
x =
-1 2 3 7
y =
5 4 2 3
m =
1 -2 1 -1
y =
1 0.925926 0.740741 0.5 0.259259 0.0740741 0
y =
0 0.115741 0.148148 0.125 0.0740741 0.0231481 0
y =
-0 -0.0231481 -0.0740741 -0.125 -0.148148 -0.115741 0
y =
0 0.0740741 0.259259 0.5 0.740741 0.925926 1
y =
1 0.5 0
y =
0 0.125 0
y =
-0 -0.125 0
y =
0 0.5 1
y =
1 0.957031 0.84375 0.683594 0.5 0.316406 0.15625 0.0429688 0
y =
0 0.0957031 0.140625 0.146484 0.125 0.0878906 0.046875 0.0136719 0
y =
-0 -0.0136719 -0.046875 -0.0878906 -0.125 -0.146484 -0.140625 -0.0957031 0
y =
0 0.0429688 0.15625 0.316406 0.5 0.683594 0.84375 0.957031 1
6 |-----------------------------------------------------------------------|
| + + + + |
| ********* |
| *** * |
| ** * |
5 |-+ * * +-|
| * |
| * |
| * |
| * |
4 |-+ # +-|
| # |
| # $$$$$$$$$$$ |
| # $$ $$$ |
| # $$$ $ |
3 |-+ # $$ $ +-|
| # $ |
| ## $ |
| ## $$ |
| + + $$ + + |
2 |-----------------------------------------------------------------------|
-2 0 2 4 6 8
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