, , , . , . . MATLAB .
. MATLAB . , :
polyfit (x, y, n) () n, ().
f(x) . , . . .
, , , . , , spline () ().
interpl:
y i = interp1 (x, y, xi) y i, , xi y. , y.
yi = interp1 (x, y, xi , method) method :
'nearest' ;
'linear' ( );
'spline' -;
'cubic' 'pchip' .
. . - :
yi = spline (x, y, xi) , , xi, .
. , , ( ) (.6.1).
MATLAB 6.5 , . Property Editor. Tools :
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Basic Fitting ();
Data Statistics .
Basic Fitting , : , 1 ( ) 10. 2 ( ) 3 ( ) (.6.2).
6.1
6.2
Data Statistics (.6.3).
6.3
(). , , :
(2)
.
t , . b .
MATLAB . . , , ode45, ode23:
ode45 - 4- 5- . , .
ode23 - 2- 4- .
:
options , odeset ( , );
tspan , [ t0 tfinal ]. t 0, t l,..., t final ( ) tspan = [ t 0 t l... t final];
0 ;
pi, 2,.. , F;
, Y Y, , - .
:
[ T, Y ] = solver (@F,tspan, 0) solver '= F (t, y) tspan 0, @F ODE-. Y , - ;
[ T, Y ] = solver (@F, tspan, y0, options) , , , options, odeset.
MATLAB :
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1) m. :
function dy = solverDE(t, y)
dy = zeros(n, 1);
dy(1) = f1 (t, y(1), y(2), , y(n));
dy(2) = f2 (t, y(1), y(2), , y(n));
dy(n) = fn (t, y(1), y(2), , y(n));
2) :
>> [T, Y] = solver(solverDE, [t0 tfinal], [y10 y20 yn0]);
>> plot(T, Y)
, , :
(3)
.
:
(4)
1(0)=1, 2(0)=1, 3(0)=1.
, ex21 ( 6.4):
6.4
ode45, [1,1,1] [0,20] ( 6.5)
>> y0=[1 1 1 ];
>> tspan=[0 20];
>> [T,Y]=ode45('ex21',tspan,y0);
>> plot(T,Y)
6.5
MATLAB dsolve, :
y= dsolve ('Dy(x)'), D() , dsolve .
y= dsolve ('Dy(x)', ''), D() , .
D, D2 . dsolve . :
[f,g] = dsolve ('Df(x),Dg(x)', ''), Df(x),Dg(x) , .
(3) dsolve ( 6.6).
6.6 dsolve
1. 6.1.
2. 6.1.
6.1
X | |||||||||
Y | 2.5 | 5.5 | |||||||
X | |||||||||
Y | -1 | -0.5 | 6.5 | 11.5 | |||||
X | |||||||||
Y | 0.5 | 2.5 | 8.5 | 9.5 | 17.5 | ||||
X | |||||||||
Y | |||||||||
X | |||||||||
Y | -2 | ||||||||
X | |||||||||
Y | -22 | -14 | -2 | ||||||
X | |||||||||
Y | 6.5 | 7.5 | |||||||
X | |||||||||
Y | 2.5 | 14.5 | 38.5 | 74.5 | |||||
6.1 | |||||||||
X | |||||||||
Y | -1 | ||||||||
X | |||||||||
Y | -2 | 0.82 | 1.46 | 2.47 | 2.9 | 3.29 | |||
X | |||||||||
Y | 2.5 | 14.5 | 38.5 | 74.5 | |||||
X | |||||||||
Y | 0.5 | 2.5 | 8.5 | 9.5 | 17.5 | ||||
X | |||||||||
Y | -1 | ||||||||
X | |||||||||
Y | -22 | -14 | -2 | ||||||
X | |||||||||
Y | 2.5 | 5.5 |
3. [ a, b ] , . 6.2. .
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6.2
a | b | ||||
1.5 | |||||
-3 | -2 | ||||
6.2 | |||||
4. , 6.3, dsolve.
6.3
1.5 | 1.5 | ||||
-1 | -1.5 | ||||
1.5 | 1.5 | ||||
1.5 | |||||
0.5 | 1.5 | -1 | |||
0.5 | |||||
-1 | |||||
1.5 | |||||
-1 | |||||
-1 | -1.5 | ||||
1.5 | 1.5 | -1 | -1 | ||
-1 | 1.5 | ||||
6.3 | |||||
0.5 | -1 | ||||
-2 | |||||
-1 |
1. .
2. .
3. .
1. interp1?
2. - MATLAB?
3. ?
7