How to solve an ODE system with time-dependent variables in MATLAB?

I'm trying to solve an ODE system with time-dependent variables in MATLAB.

function dPdt = ode_Core1(~,P,landa,P_L,P_R)
    dPdt = zeros(5,1);
    dPdt(1) = 4*lambda*(-3*P(1) + P(2) + 2*P_L)/3;
    dPdt(2) = lambda*(P(1) - 2*P(2) + P(3));
    dPdt(3) = lambda*(P(2) - 2*P(3) + P(4));
    dPdt(4) = lambda*(P(3) - 2*P(4) + P(5));
    dPdt(5) = 4*lambda*(P(4) - 3*P(5) + 2*P_R)/3;

Where "lambda" is a time-dependent variable and should be calculated having P values at previous times. I have worked with "ode45" but I'm not quite sure this case can be solved using ode45. Can anyone help me with this?

[madhan ravi]

Could you post the equation?

[Mohammad Khojastehmehr]

The general form is dP/dx=alpha*d2P/dx2

It is a diffusion problem. However, it is a little modified in my case. I was trying to apply the method of lines.

Answer 1

[Star Strider]

One method of doing that is in ODE with Time-Dependent Terms using linear interpolation. However to do that you would have to pass the time variable to ‘ode_Core1’. In the code you posted, you are not.

[Mohammad Khojastehmehr]

Thank you for your help. However, for some reasons, I can't use linear interpolation. To be specific, to calculate the pressure field (p(1) to p(5)) at time t=t1, alpha must be known at time t=t0 and we have alpha at t=t0 so I don't have any problem. However, to calculate the pressure field at time t=t2, I should have the value of alpha at t=t1 and since we don't have alpha values, it must be calculated right after the pressure field at t=t1 is calculated and this is my problem. Aren't there any other options available aside from Interpolation?

[Mohammad Khojastehmehr]

Sorry instead of lambda I said alpha.

[Star Strider]

Does alpha or lambda or whatever have any sort of specific expression?

Is it a vector or a function?

What specifically do you want from it?

Answer 2

[Steven Lord]

From your description, it sounds like you don't have an ordinary differential equation (ODE) but you have a delay differential equation (DDE). Take a look at the dde23 function.