I want to write a script that reads an input text file that specifies the parameters and then uses them to solve an integral

I want to write a script that reads an input text file that specifies the parameters:

a:1

b:2

c:3

d:4

x0:1

y0:1

tf:25.

Then integrate a system of equations given the parameters read from the input text file. Sytem should be integrated from t=0 to t=tf. After plot x(t) and y(t) in a single graph.

This is what I did. It gives me errors. Kindly tell me what i am doing wrong and how to solve the question. Thanks.

[q,w] = readvars('variables.txt');

a = w(1);
b = w(2);
c = w(3);
d = w(4);
x0 = w(5);
y0 = w(6);
tf = w(7);
t = 0;

x = linspace(t,tf,25);
fx = @(x,y) a*x-b*x*y;
fy = @(y,x) c*x*y-d*y;

x = linspace(t,tf,25);
for i = 1:length(x)
    fx(i)= integral(@(x)(fx(x,y)),t,x(i));
end 

y = linspace(t,tf,25);
for k = 1:length(y)
    fy(k)= integral(@(y)(fy(y,x)),t,y(k));
end 
figure (1)
plot(fx)
plot(fy)

[Torsten]

You have a system of differential equations. Use one of the ODE-integrators to solve it (e.g.ODE45, ODE15S).

"integral" is not suited in this case.

[Gideon Sarpong]

I improved the code to this and i do not get errors but shows this plot.

[q,w] = readvars('variables.txt');

a = w(1);
b = w(2);
c = w(3);
d = w(4);
x0 = w(5);
y0 = w(6);
tf = w(7);
t = 0;


    a = w(1);
    b = w(2);
    y = 0.5;
    fx = @(x) a*x-b*x*y;
    format long
    fx = integral(fx,t,tf,'RelTol',1e-8,'AbsTol',1e-13,'ArrayValued',true); 


    c = w(3);
    d = w(4);
    x = 4/3;
    fy = @(y) c*x*y-d*y;
    format long
    fy = integral(fy,t,tf,'RelTol',1e-8,'AbsTol',1e-13,'ArrayValued',true);
    
figure (1)
plot(fx,'*')
hold on
plot(fy)

[Torsten]

I can only repeat: you can't use "integral" to solve differential equations that depend in the dependent variable.

You must use one of the ode integrators or try "dsolve".

Answer 1

[Fabio Freschi]

As suggested by @Torsten your problem is a system of first order ODEs and you must use a ODE integrator. Try this

clear variables, close all

% your params (you can instead load here your file)
a = 1;
b = 2;
c = 3;
d = 4;
x0 = 1;
y0 = 1;
tf = 25;

% define the system of ODE as anonymous function.
% The vector variable is here X, with X(1) = x, X(2) = y
odeFun = @(t,X)[a*X(1)-b*X(1)*X(2); c*X(1)*X(2)-d*X(2)];

% initial value
X0 = [x0; y0];

% time interval
tSpan = [0 tf];

% solution with ODE45
[t,X] = ode45(odeFun,tSpan,X0);

figure
plot(t,X)
xlabel('time');
legend('x','y')