How to solve an ODE with an array using ODE45?

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DIP
DIP el 20 de Feb. de 2017
Comentada: DIP el 6 de Mzo. de 2017
I have an ODE, udY/dx=S , where Y and S are arrays , how do I solve it using ODE45 ???
  3 comentarios
DIP
DIP el 20 de Feb. de 2017
Editada: DIP el 20 de Feb. de 2017
velocity. its constant
Jan
Jan el 20 de Feb. de 2017
@DIP: Please provide more details. "velocity" does not help, because Matlab does not care about the physical meaning of variables. Post the function you want to integrate, preferrably in valid Matlab code. If it is written correctly, all you have to do is calling ode45.

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DIP
DIP el 6 de Mzo. de 2017
% Solution 4: Chemical Species Concentration as a Function of Axial Distance
clc
clear
% Constants
L = 0.12;
N = 39;
T(1:N) = 750;
delx = L/(N-1);
xspan = 0:delx:0.12;
C0 = [0.52 0.99 0.0];
% ODE 45 Code
[x,C]=ode45('hw2_4',xspan,C0);
% Plots
subplot(2,1,1);
plot(x,C(:,1),'b--o',x,C(:,2),'g--+',x,C(:,3),'r--s')
legend('C_{CO}','C_{O2}','C_{CO2}')
xlabel('Axial (x) Direction [m]')
ylabel('Concentrations [mol/m^3]')
title('Molar Concentration vs Distance')
Function File:
function dcdx=hw2_4(x,C)
% Constants
u = 1.5;
A = 2.2e10;
Ea = 130000;
Ru = 8.3145;
T = 750;
% Rate Constants
R(1) = -A * (exp(-Ea / (Ru*T))) * C(1) * sqrt(C(2));
R(2) = 0.5 * R(1);
R(3) = -R(1);
dcdx = [R(1);R(2);R(3)]/u;

Más respuestas (2)

Jan
Jan el 20 de Feb. de 2017
Editada: Jan el 21 de Feb. de 2017
ode45 works with vectors, therefor if Y is a vector, the provided examples in the docs should help: https://www.mathworks.com/help/matlab/ref/ode45.html#examples . If not, please post more details by editing the question.
[EDITED, Considering your comments] Perhaps you mean this:
function main
% Initial Conditions
Cco(1) = 0.52; %Y1
Co2(1) = 0.99; %Y2
Ch2o(1) = 0; %Y3
L = 0.12;
N = 39;
delx = L/(N-1);
x = 0:delx:0.12;
C0 = [Cco; Co2; Ch2o];
[x,C] = ode45(@DiffEQ, x, C0);
plot (x,C)
end
function dC = DiffEQ(x, C)
u = 1.5;
A = 2.2e10;
Ea = 130;
Ru = 8.3145;
T = 750;
Cco = C(1);
Co2 = C(2);
Ch2o = C(3);
Rco = -A * (exp(-Ea / (Ru*T))) * Cco * sqrt(Co2); %S1
Ro2 = 0.5 * Rco; %S2
Rh2o = -Rco; %S3
dC = [Rco; Ro2; Rh2o] / u;
end
This needs a lot of processing time. Using ode15s was successful in less than a second (are you sure the system is not stiff). The diagram looks nicer, if you define:
x = [0, 0.12];
  10 comentarios
DIP
DIP el 21 de Feb. de 2017
I think its got to do with defining the arrays of C and R correctly.
Jan
Jan el 21 de Feb. de 2017
@DIP: @(x,C) R/u is constant. Changes in the coordinates are not considered, because all calls of "R/u" reply the same value. Better use a normal function instead of a anonymous function. I've showed you already, how to do this.
Concerning:
documentation for the last line of your main function
do you mean "plot(x,C)"?

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Star Strider
Star Strider el 20 de Feb. de 2017
See if the approach in Monod kinetics and curve fitting will do what you want.
You will have to adapt it to your data and differential equations. The essential design should work.

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