State Vectorization for ODE 45

Question

shahin sharafi about 14 hours 前

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/2149414-state-vectorization-for-ode-45

编辑： Walter Roberson about 10 hours 前

Hi all.

I'm trying to model a dyanmical system as following using vectorization of state for ODE45. My model includes three states that for two system there will be 6 states all in all. However, for some reason I'm gonna model these states by vectorization of states for solving by ODE45. However, as I checked the resutls, results are slightly different with respect to each other. Can you help why vectorization causes such these differences in the results? Thank you in Advance.

First code is as below:

clear all;clc;
%%
global b r I x0 
b=3.0;
r=0.02;
I=2.8;
x0=-1.6;
initial_condition=[-1,0.2,0.4,0.5,0,-0.2];
tspan=[0 3000];
options = odeset('RelTol', 1e-6, 'AbsTol', 1e-8);
[t,y]=ode45(@EquationSys,tspan,initial_condition);
figure(1)
plot(t,y(:,1))
hold on
%%
function dy=EquationSys(t,y)
global b r I x0 
x1=y(1);
y1=y(2);
z1=y(3);
x2=y(4);
y2=y(5);
z2=y(6);
dy=[y1-x1^3+b*x1^2-z1+I;
    1-5*x1^2-y1;
    r*(4*(x1-x0)-z1);
    y2-x2^3+b*x2^2-z2+I;
    1-5*x2^2-y2;
    r*(4*(x2-x0)-z2);
    ];
end
%%

And Second code for vectorization is :

clear all;clc;
%%
global b r I x0 
b=3.0;
r=0.02;
I=2.8;
x0=-1.6;
initial_condition=[-1,0.2,0.4,0.5,0,-0.2];
tspan=[0 1000];
options = odeset('RelTol', 1e-6, 'AbsTol', 1e-8);
[t,state]=ode45(@EquationSys,tspan,initial_condition);
figure(1)
plot(t,state(:,1))
hold on
%%
function dy=EquationSys(t,state)
global b r I x0 
x=state(1:2);
y=state(3:4);
z=state(5:6);
dy=[y-x.^3+b.*x.^2-z+I;
    1-5.*x.^2-y;
    r.*(4.*(x-x0)-z);
    ];
end
%%

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Shashi Kiran about 13 hours 前

在 MATLAB Online 中打开

Hi @shahin sharafi,

After analyzing your code, I made some simple adjustments to the vectorized function to work as expected:

function dy=EquationSys(t,state)
global b r I x0 
x=state([1, 4]);
y=state([2, 5]);
z=state([3, 6]);
dy=zeros(6,1);
dy([1, 4]) = y - x.^3 + b.*x.^2 - z + I;
dy([2, 5]) = 1 - 5.*x.^2 - y;
dy([3, 6]) = r.*(4.*(x-x0) - z);
end

Hope this helps!

shahin sharafi about 12 hours 前

Thank you so much! it works

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Answer 1

Shivam Gothi about 13 hours 前

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/2149414-state-vectorization-for-ode-45#answer_1508484

编辑：Shivam Gothi about 13 hours 前

在 MATLAB Online 中打开

Hello @shahin sharafi,

This happened because your state vector in case-1 is:

For the system of equations to give the same output their initial conditions should match. Therefore,just change the initial_condition vector in case 2 (Vactorised approach) as:

initial_condition=[-1,0.5,0.2,0,0.4,-0.2];

This will result in same solution for both the cases. I have attached the plot below. (Note:- there are two graphs, but they coincided exactly)