confusion on a new schema for solving ode
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Hello all, recently i've been working on an algorithm for solving ode, called QSS family, which was found by Prof.Ernesto Kofman. I want to run the algorithm on matlab code, but i'm not sure if the code is right. Can anyone help me to tell if it's right?
The code below is an example to solve the ode:, with and all equal 0 at .
clc
clear
tic
delta_q=1e-4;
q1=0;q2=0;
x1=0;x2=0;
t=0;delta_t=0;tfinal=20;
A=zeros(0,3);
n=0;
while (t<tfinal)
Dx1=q2;
Dx2=1-3*q1-4*q2;
if (Dx1>0)
delta_x1=delta_q+q1-x1;
else
delta_x1=delta_q-q1+x1;
end
if (Dx2>0)
delta_x2=delta_q+q2-x2;
else
delta_x2=delta_q-q2+x2;
end
delta_t1=delta_x1/abs(Dx1);
delta_t2=delta_x2/abs(Dx2);
if (delta_t1<delta_t2)
delta_t=delta_t1;
t=t+delta_t;
x1=x1+Dx1*delta_t;
x2=x2+Dx2*delta_t;
q1=x1;
else
delta_t=delta_t2;
t=t+delta_t;
x1=x1+Dx1*delta_t;
x2=x2+Dx2*delta_t;
q2=x2;
end
n=n+1;
A(n,1)=t;
A(n,2)=x1;
A(n,3)=x2;
% A(n,4)=q1;
% A(n,5)=q2;
end
A;
figure(1)
plot(A(:,1),A(:,2),A(:,1),A(:,3));
toc
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Réponse acceptée
Bobby Fischer
le 15 Jan 2021
Hello,
function euler1
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
clc
clear
tic
delta_q=1e-4;
q1=0;q2=0;
x1=0;x2=0;
t=0;delta_t=0;tfinal=20;
A=zeros(0,3);
n=0;
while (t<tfinal)
Dx1=q2;
Dx2=1-3*q1-4*q2;
if (Dx1>0)
delta_x1=delta_q+q1-x1;
else
delta_x1=delta_q-q1+x1;
end
if (Dx2>0)
delta_x2=delta_q+q2-x2;
else
delta_x2=delta_q-q2+x2;
end
delta_t1=delta_x1/abs(Dx1);
delta_t2=delta_x2/abs(Dx2);
if (delta_t1<delta_t2)
delta_t=delta_t1;
t=t+delta_t;
x1=x1+Dx1*delta_t;
x2=x2+Dx2*delta_t;
q1=x1;
else
delta_t=delta_t2;
t=t+delta_t;
x1=x1+Dx1*delta_t;
x2=x2+Dx2*delta_t;
q2=x2;
end
n=n+1;
A(n,1)=t;
A(n,2)=x1;
A(n,3)=x2;
% A(n,4)=q1;
% A(n,5)=q2;
end
figure(1)
close(1)
figure(1)
subplot(1,3,1)
hold on
axis([0,20 -0.05 0.35])
plot(A(:,1),A(:,2),'b')
plot(A(:,1),A(:,3),'r');
grid on
title('HS')
toc
whos
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
t=linspace(0,20,501);
x0=[0 0];
whos
[t,x]=ode45(@fun,t,x0);
whos
subplot(1,3,2)
hold on
axis([0,20 -0.05 0.35])
plot(t,x(:,1),'k')
plot(t,x(:,2),'k')
grid on
title('edo45')
subplot(1,3,3)
hold on
axis([0,20 -0.05 0.35])
plot(A(:,1),A(:,2),'b')
plot(A(:,1),A(:,3),'r');
plot(t,x(:,1),'k.')
plot(t,x(:,2),'k.')
grid on
title('HS, edo45')
function [dxdt]=fun(~,x)
x1p=x(2);
x2p=1-3*x(1)-4*x(2);
dxdt=[x1p; x2p];
end
end
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