multistep method 求解数值常微分方程——matlab程序
本帖最后由 博大广阔 于 2011-11-18 20:41 编辑%the local error of the adams bashforth computer by a method is o(h^5)
%compare with fourth_order runge-kutaa method,a multistep method requires
%only one new function evalution for each step .this can lead to great
%saving in time and expense.
function multistep_method=multistep_method()
clear all
close all
%%%%%%%%%%%%%%%%%%%%%%%%%algorithm parameter and the initial value
x10=; %state vector of initial value
%should be modify for different system
u=0; %control law
t=0; h=0.2; tmax=10; %simulation time and step length
%%%%%%%%%%%%%%%%%%%%%四阶龙格计算初始四个值%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
XX(:,1)=x10; time(1)=0;
for n=2:1:4
=derives(t,x10,u);if n==2; yy(:,1)=dX;end
m1=h*dX; t=t+0.5*h;X=x10+0.5*m1; %更新导数
=derives(t,X,u);
m2=h*dX; X=x10+0.5*m2; %更新导数
=derives(t,X,u);
m3=h*dX; t=t+0.5*h; X=x10+m3; %更新导数
=derives(t,X,u);
m4=h*dX;
x10=x10+(1/6)*(m1+2*m2+2*m3+m4);
XX(:,n)=x10;time(n)=t; %存输出值
=derives(t,x10,u); yy(:,n)=dXa;
end
%%%%%%%%%%%%%%%%%%%%%%%%%%multistep initial value %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
YY(1:4)=XX(1,:);
Xold=XX(:,4); %state vector
y0=yy(:,1);y1=yy(:,2);y2=yy(:,3);y3=yy(:,4); %存导数
n=5; %loop needed paramter use as save the output result
while t<tmax
%%%%%%%%%%%%%%%%%%%%%%%%%multistep method%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
aa=Xold+h*(55*y3-59*y2+37*y1-9*y0)/24; t=t+h;
=derives(t,aa,u);
Xold=Xold+h*(9*y4+19*y3-5*y2+y1)/24;
y0=y1;y1=y2;y2=y3;y3=y4; %rewrite the parameter ！！！！！认真点，，，，
YY(n)=Xold(1) %output which should be modify for different system
time(n)=t; n=n+1;
end
plot(time,YY,'r') ;grid on
end
function =derives(t,X,u)
%fi=cos(3*t);u=0;
%A=; B=;
dX=t+X-1;
end
这个程序的用处是？ 这个是常微分方程里面的多重打靶法吗？
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