MATLAB: How to integrate this function using ode23

MATLABode23

The given function is as follows:

I've written the following code:

clc
clear all
tspan = [0 10];
y0 = 0;
%[t,y] = ode23(@(t,y) 2*t, tspan, y0);
Minc =  67;
Mp = 12;
dfe = 7200;
din = 4040;
Dp = 5e-5;
Cl = 0.045;
Cleq = 0.005;
z = (Minc/(100*Mp))*(dfe/din)*Dp*(Cl - Cleq) ;
disp( z)
[t,y] = ode23(@(t,y) (1/y)*(Minc/(100*Mp))*(dfe/din)*Dp*(Cl - Cleq), tspan, y0);
plot(t,y,'-o');

Best Answer

Although I couldn't figure out the actual cause of this issue, the error is caused by setting the initial condition to zero. It can be resolved by giving a tiny value to the initial condition. For example,

y0 = 1e-308; % minimum possible exponent for double

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MATLAB: 4th order Runge-Kutta code that can solve for several intial conditions

Here's a version:

% Initial conditions
t0=0;
x0=0:0.2:1;
y0=1:0.2:2;
dt=0.1;
tz=1;
t_range= t0:dt:tz;
X = zeros(numel(x0),numel(t_range));
Y = zeros(numel(y0),numel(t_range));
x_rk=zeros(1,numel(t_range));
y_rk= zeros(1,numel(t_range));
for n = 1:numel(x0)
    x_rk(1)=x0(n);
    y_rk(1)=y0(n);
    for i=1:length(t_range)-1
        [x_rk(i+1), y_rk(i+1)]=rk_method(x_rk(i),y_rk(i),dt);
    end
    X(n,:) = x_rk;
    Y(n,:) = y_rk;
    %% PLots
    subplot(numel(x0)/2,2,n)
    plot (t_range, x_rk,'b-o',t_range, y_rk,'y-o','MarkerSize',5);
    grid
    title([num2str(x0(n)),'   ',num2str(y0(n))])
    legend('x','y')
end
disp('X = '), disp(X)
disp('Y = '), disp(Y)
%% Functions
function [dxdt, dydt]= f(x,y)
dxdt =  5*x-3*y;
dydt = -6*x+2*y;
end 
function [x1, y1]=rk_method(x0,y0,dt)
[k11, k12]=f(x0,y0);     
[k21, k22]=f(x0+0.5*dt*k11,y0+0.5*dt*k12); 
[k31, k32]=f(x0+0.5*dt*k21,y0+0.5*dt*k22); 
[k41, k42]=f(x0+dt*k31, y0+dt*k32); 
x1=x0+dt*((k11/6)+((k21+k31)/3)+(k41/6));
y1=y0+dt*((k12/6)+((k22+k32)/3)+(k42/6));
end

MATLAB: Error using exp Too many input arguments.

The exp function doesn’t like the comma (,) as a decimal separator. Change it to a (.).

With that modification, this works:

tspan = [0 1500];
y0 = 0;
[t,y] = ode45(@(t,y) exp(-0.0001/8.314./(300+4000.*y./(421.8-7.8.*y))), tspan, y0);
plot(t,y)

Best Answer

Related Solutions

MATLAB: 4th order Runge-Kutta code that can solve for several intial conditions

MATLAB: Error using exp Too many input arguments.

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