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

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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)
  3 Commenti
Gideon Sarpong
Gideon Sarpong il 14 Dic 2022
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
Torsten il 14 Dic 2022
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".

Accedi per commentare.

Risposta accettata

Fabio Freschi
Fabio Freschi il 16 Dic 2022
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')

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