ODE with Initial Conditions - Electroporation

I have to solve the following ODE equation. I have all the variables imported into code already (including Ur). I have to solve the ODE for when Vm = 0, 0.3, 0.45,0.5,0.6 for two separate initial conditions: r=1E-8 and r=5E-10.

I then have to graph each Vm for each r (for a total of 10 plots).

All I was provided was:

options=odeset('MaxStep',1e-7);

tspan=[0 1e-3];

This is my code:

%Electroporation Project

sym vars

D=5E-14; %diffusion coefficient for pore radius

kB=1.38E-23; %boltzmann constant

T=310; %temperature

F=0.70E-9; %max electric force

rh = 0.97E-9; %velocity constant

rt = 0.31E-9; %velocity constant

B=1.4E-19; %steric repulsion energy (beta)

rs = 0.51E-9; %minimum radius of hydrophilic pores (r star)

g=1.8E-11; %edge energy (gamma)

s=-1E-4; %sigmaeff

r1=1E-8; %10 nm initial condition 1

r2 = 5E-10; %0.5nm initial condition 2

V = 0; %solving ODE for these values for both r1 and r2

%Equation dr/dt=Ur

U1=(D/kB*T)

U2=((V^2*F)*(r1+rt)/(1+rh))

U3=(4*B)*(rs/r1)^4*(1/r1)-2*pi*g+2*pi*s*r1

U=(U1*(U2+U3))

options=odeset('MaxStep',1e-7);

tspan=[0 1e-3];

[t,U] =ode45(@(t,U) U,tspan,r1, options)

figure

plot(t,U)

xlabel('t')

ylabel('U')

legend('Vmax=0, r1=10nm')

Can someone please help me.

[Star Strider]

Post what you have coded.

Note that the ode45 call should be (in the for loop that passes the requisite values for ‘Vm’):

[t{j},r{j}] =ode45(@(t,U) U(t,r,Vm(j),sigmaeff), tspan, r1, options);

Change that to conform to your existing code for ‘U’.

[Nasir Holliday]

updated with my code