Runge-Kutta method to solve differential equations

Continuous problem, differential equations or partial differential equations must be able to express. Such as the spread of disease, and other news media.

Discrete problem, you can use differential equations or algorithms similar difference.

equation

$ Y '= cos t $

Code

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clear,clc; @ = F (t, Y) COS (t); tspan = [ 0 , 2 * PI]; % range of time t yO = 2 ; initial value for the% y, C integrator for processing obtained [t, y] = ode23 (F, tspan, yO); % Note call format Plot (T, Y); the xlabel ( 'T' ); ylabel ( 'Y' );

@He represents the handle, when the function as a parameter to another function, this time must be used handle. Here is the function fto the function ode23.

result

Solving higher order differential equations

equation

$begin{equation}
left{
begin{array}{r1}
y’’=-sin y+sin 5t\
y(0)=1\
y’(0)=0\
end{array}
right.
end{equation}$

可以将该高阶微分方程转化为两个一阶的微分方程：$begin{equation}
left{
begin{array}{r1}
y_1=y\
y_2=y’\
y’_1=y_2\
y’_2=-sin y_1+sin 5t\
y_1(0)=1\
y_2(0)=0\
end{array}
right.
end{equation}$

代码

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clear,clc; @ = F (T, Y) [Y ( 2 ); -sin (Y ( . 1 )) + SiN ( . 5 * T)]; % are the two parameters y1 and y2 of the derivative tspan = [ 0 , 20 is ]; % range of time t yO = [ . 1 ; 0 ]; % initial value, corresponding to y1, y2 initial value [t, Y] = ode23 (F, tspan, yO); % Note call format plot (t, y); the xlabel ( 'T' ); ylabel ( 'Y' ); Legend ( 'Y1' , 'Y2' );

result

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Author: @ smelly salted fish

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