Delay differential equation - Error: Function definition not supported in this context. Create functions in code file.

I am trying to solve delay differential equations. I am using matlab online. I can not figure out what is wrong in my code. Could someone please help me?! thanks.

function ddex2
    
    p.alpha_m = 1e-2;
    p.alpha_M = 7e-2;
    p.beta_c = 3e-2;
    p.beta_e = 3e-2;
    p.s = 5e-4;
    p.rho = 5e-3;
    p.gamma = 0.01;
    p.lamb = 100;
    p.kappa = 1.5;
    p.nu = 167e-7;
    p.epsilon = 0.0001;
    tau     = 40;
    
    x_c0 = 1000;
    x_e0   = 1;
    B10 = 300;
    B20 = 0;
    
    %history = [x_c0; x_e0; B10; B20];
    tau     = 40;
    
    function s = ddex2hist(t)
        % Constant history function for DDEX1.
        s = ones(1000,1,300,0);
        
        sol = dde23(@ddex2de,tau,@ddex1hist,[0, 1000]);
        
        figure
        plot(sol.x,sol.y(2,:))
        title('Time delay')
        xlabel('time t')
        ylabel('x_e(t)')
        
        
        % -----------------------------------------------------------------------
        %
        
        function dydt = ddex2de(y,Z)
            % Differential equations function for DDEX2.
            w_th = p.rho*x_c + p.kappa*p.rho*x_e;
            if w_th ~= 0
                C_c = min(1, w/w_th)*p.s*x_c;
                C_e = min(1, w/w_th)*p.kappa*p.s*x_e;
            else
                C_c = p.s*x_c;
                C_e = p.kappa*p.s*x_e;
                if (x_c ~= 0) && (p.s ~= 0)
                    alpha_c = p.alpha_m + max(array([0, 1 - C_c/(p.s*x_c)]))*(p.alpha_M - p.alpha_m);
                else
                    alpha_c = p.alpha_m;
                    if (x_e ~= 0) && (p.s ~= 0)
                        alpha_e = p.alpha_m + max(array([0, 1 - C_e/(p.s*x_e)]))*(p.alpha_M - p.alpha_m);
                    else
                        alpha_e = p.alpha_m;
                    end
                    
                    ylag = Z(:,2);
                    x_etau = ylag(2);
                    x_c = y(1);
                    x_e = y(2);
                    B1  = y(3);
                    B2  = y(4);
                    dx_cdt = (p.beta_c - alpha_c)*x_c;
                    dx_edt = (p.beta_e*x_etau) - (alpha_e*x_e);
                    dB1dt = p.gamma*B1*(p.lamb - B1) - p.nu*x_c*B1;
                    dB2dt = p.nu*x_c*B1 - C_c - C_e - p.epsilon*B2;
                    dydt = [ dx_cdt
                        dx_edt
                        dB1dt
                        dB2dt];
                end
                % -----------------------------------------------------------------------
                
            end  % ddex2

Answer 1

[Sahithi Metpalli]

Hi,

I assume that you are creating the function from MATLAB command prompt and it is not supported.

You can create the function in MATLAB Online as follows:

Go to Home tab and select New Script and write the function in the script file with the file name same as the function

[Naghmeh Akhavan]

Hello Sahithi, Thank you for response. I have changed the name of function and saved the file with same name. But after runnig, I have no result or even error. Should I do something else? Thanks!

function delayfunc
    
    p.alpha_m = 1e-2;
    p.alpha_M = 7e-2;
    p.beta_c = 3e-2;
    p.beta_e = 3e-2;
    p.s = 5e-4;
    p.rho = 5e-3;
    p.gamma = 0.01;
    p.lamb = 100;
    p.kappa = 1.5;
    p.nu = 167e-7;
    p.epsilon = 0.0001;
    tau     = 40;
    
    %x_c0 = 1000;
    %x_e0   = 1;
    %B10 = 300;
    %B20 = 0;
    
    %history = [x_c0; x_e0; B10; B20];
    tau     = 40;
    
    function s = history(t)
        % Constant history function for DDEX1.
        s = ones(1000,1,300,0);
        
        sol = dde23(@ddex2de,tau,@history,[0, 1000]);
        
        figure
        plot(sol.x,sol.y(2,:))
        title('Time delay')
        xlabel('time t')
        ylabel('x_e(t)')
        
        
        % -----------------------------------------------------------------------
        %
        
        function dydt = ddex2de(y,Z)
            % Differential equations function for DDEX2.
            w_th = p.rho*x_c + p.kappa*p.rho*x_e;
            if w_th ~= 0
                C_c = min(1, w/w_th)*p.s*x_c;
                C_e = min(1, w/w_th)*p.kappa*p.s*x_e;
            else
                C_c = p.s*x_c;
                C_e = p.kappa*p.s*x_e;
                if (x_c ~= 0) && (p.s ~= 0)
                    alpha_c = p.alpha_m + max(array([0, 1 - C_c/(p.s*x_c)]))*(p.alpha_M - p.alpha_m);
                else
                    alpha_c = p.alpha_m;
                    if (x_e ~= 0) && (p.s ~= 0)
                        alpha_e = p.alpha_m + max(array([0, 1 - C_e/(p.s*x_e)]))*(p.alpha_M - p.alpha_m);
                    else
                        alpha_e = p.alpha_m;
                    end
                    
                    ylag = Z(:,2);
                    x_etau = ylag(2);
                    x_c = y(1);
                    x_e = y(2);
                    B1  = y(3);
                    B2  = y(4);
                    dx_cdt = (p.beta_c - alpha_c)*x_c;
                    dx_edt = (p.beta_e*x_etau) - (alpha_e*x_e);
                    dB1dt = p.gamma*B1*(p.lamb - B1) - p.nu*x_c*B1;
                    dB2dt = p.nu*x_c*B1 - C_c - C_e - p.epsilon*B2;
                    dydt = [ dx_cdt
                        dx_edt
                        dB1dt
                        dB2dt];
                end
                % -----------------------------------------------------------------------
                
            end  % ddex2