Errors In User Defined Function for Solving ODE System

I'm trying to create a function to solve a system of ode's using ode45.

1. 
2. 

With Initial Conditions: ,

and where , , , , , ,

The functions u and v are column vectors with 101 entries

The errors I'm getting are:

Not enough input arguments.

Error in ODESolver/ODEsystem (line 22)

dpdt = -Zeta*p*log(p/q)-Theta*p*v;

Error in odearguments (line 92)

f0 = ode(t0,y0,args{:}); % ODE15I sets args{1} to yp0.

Error in ode45 (line 107)

odearguments(odeIsFuncHandle,odeTreatAsMFile, solver_name, ode, tspan, y0, options, varargin);

Error in ODESolver (line 5)

[tSol, XSol] = ode45(@ODEsystem,t,IC);

Code:

Code to run the function:

p0 = 1;
q0 = 1;

[tSol, XSol] = ODESolver(u,v,t,p0,q0);

Unrecognized function or variable 'u'.

Ode Function/Solver

function [tSol,XSol] = ODESolver(u,v,t,p0,q0)

IC = [p0,q0]; 

[tSol, XSol] = ode45(@ODEsystem,t,IC);

  pTTumorEndVolume = XSol(end,1);

    function dXdt = ODEsystem(t,X,u,v)

 p = X(1);     
 q = X(2);      

 Theta = 0.1;       %Theta       
 Gamma = 0.15;      %Gamma      
 b = 5.85;          %b
 d = 0.00873;       %d
 Mu = 0.02;         %Mu
 Zeta = 0.084;      %Zeta
 Eta = 0;           %Eta

dpdt = -Zeta*p*log(p/q)-Theta*p*v;                          
dqdt = (b*p)-(Mu*q)-(d*(p)^(2/3)*q)-(Gamma*u*q)-(Eta*q*v);

dXdt = [dpdt;dqdt];
    end

end

Answer 1

[Star Strider]

You need to tell ode45 what arguments it needs to use:

[tSol, XSol] = ode45(@(t,x)ODEsystem(t,x,u,v),t,IC);

It only needs to know about ‘t’ and ‘x’. The others are passed as extra parameters.

Try this —

u = rand                                                % Not Otherwise Defined

u = 0.1650

v = rand                                                % Not Otherwise Defined

v = 0.8246

t = linspace(0, 100,250);                               % Not Otherwise Defined

p0 = 1;
q0 = 1;

[tSol, XSol] = ODESolver(u,v,t,p0,q0);

figure
plot(tSol,XSol)
grid

xlabel('t')
ylable('X')

function [tSol,XSol] = ODESolver(u,v,t,p0,q0)



IC = [p0,q0]; 

[tSol, XSol] = ode45(@(t,x)ODEsystem(t,x,u,v),t,IC);

  pTTumorEndVolume = XSol(end,1);

    function dXdt = ODEsystem(t,X,u,v)

 p = X(1);     
 q = X(2);      

 Theta = 0.1;       %Theta       
 Gamma = 0.15;      %Gamma      
 b = 5.85;          %b
 d = 0.00873;       %d
 Mu = 0.02;         %Mu
 Zeta = 0.084;      %Zeta
 Eta = 0;           %Eta

dpdt = -Zeta*p*log(p/q)-Theta*p*v;                          
dqdt = (b*p)-(Mu*q)-(d*(p)^(2/3)*q)-(Gamma*u*q)-(Eta*q*v);

dXdt = [dpdt;dqdt];
    end

end

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