Out of memory error in Matlab and How to solve it?

Hello Everyone

I am trying to run a simple straightforward code in Matlab. I am having out of memory error. I am attaching the code and the error message. Can someone please point me out how can I solve this or where I am making mistakes.

Thank you.

clc
clear all
close all

T_ar=300;                                          % Temparature of Argon
k_B=1.380649e-23;                                  % Boltzmann's Constant in J/K
e=1.60217663e-19;                                  % electronic charge in Coulomb
m_e=9.109e-31;                                     % mass of an electron in kg
epsilon=8.854e-12;                                 % permittivity of free space
A_sp=.005024;                                      % Powered Electrode Area in m^2
A_sg=.007854;                                      % Grounded Electrode Area in m^2
l_B=0.075;                                         % plasma bulk length in m
n=1.96e16;                                         % plasma density in m^-3

upsilon=0.08;                                      % Symmetry Parameter
T_e=3;                                             % Electron Temparature in eV 

m_i=40;                                            % Argon mass in amu for determining bohm velocity
amu=1.660539e-27;                                  % 1 Dalton
v_B=sqrt((e*T_e)/(m_i*amu));                       % Bohm velocity
v_e = sqrt(8*k_B*T_ar/(pi*m_e));                   % mean thermal speed

p=1;                                               % pressure in pascal
n_g=(p/(k_B*T_ar));                                % gas density in m^-3                                                
Km=10^-13;
v_m=Km*n_g;                                        % momentum transfer collision frequency
v_eff=v_m+(v_e/l_B);                               % Effective Collision Rate in s^-1


J_e=e*n*v_e;                                       % Coefficient of electron current
J_i=e*n*v_B;                                       % Coefficient of ion current

Jip=J_i*A_sp;                                      % Ion current at Powered Sheath
Jig=J_i*A_sg;                                      % Ion current at Grounded Sheath
Jep=J_e*A_sp;
Jeg=J_e*A_sg;

                                    
L_pl=(l_B*m_e)/(e^2*n*A_sp);                       % Plasma Bulk Inductance
R_pl=v_eff*L_pl ;                                  % Plasma Bulk Resistance
Lpl_inv=1/L_pl;

A=(1/(2*e*epsilon*n*A_sp^2));
xx=(e*A/(T_e))
B=(1/(2*e*epsilon*n*A_sg^2));

V0=300;                                            % Amplitude of RF input voltage 
C_B=3.34e-6;                                       % Dc blocking capacitor


f = @(t,x) [-x(4)-Jip+Jep*exp(-(e*A/(T_e))*(x(1)^2));
            x(4)-Jig+Jeg*exp(-(e*B/(T_e)).*(x(2)^2));
            -(1/C_B).*x(4);
            (A.*(x(1)^2)-B.*(x(2)^2)+(V0*cos(t))+x(3))-((v_eff/Lpl_inv).*x(4))];
[t,xa] = ode45(f,[0, 10],[0,0,-62,0]);


figure(1)
plot(t,xa(:,1),'Color','blue'),grid on;
title('xa1')
xlabel('t'), ylabel('Qsp (Powered Electrode Sheath Charge)')

figure(2)
hold off
plot(t,xa(:,2),'Color','blue'),grid on;
title('xa2')
xlabel('t'), ylabel('Qsp (Grounded Electrode Sheath Charge)')

figure(3)
plot(t,xa(:,3),'Color','blue')
grid on;
title('xa3')
xlabel('t'), ylabel('Self Bias Voltage')

figure(4)
plot(t,xa(:,4),'Color','blue'),grid on;
title('xa4')
xlabel('t'), ylabel('Plasma Current')

The error message is as follows:

[Walter Roberson]

You can potentially run out of memory in ode45 if the ode is unusually rapidly changing or if it is stiff. Experiment with ode15s()

[Md. Golam Zakaria]

@Walter Roberson If I use a computer with higher ram capacity like 32 GB, will it solve the problem ?

Answer 1

[Jan]

Of course an out-of-memory problem is solved, if more RAM is available. But if the equation is stiff, this solution is of temporary nature only. Using a solver like ode15s is a better way, because ode45 will compute a huge number of steps, which let the accumulated rounding errors explode.

Use a stiff solver for stiff problems.

On the other hand it is possible, that the problem is not stiff and you simply have not enough RAM installed. A cheap (and not scientific way) to check this is using the debugger: Let the integration run a certain time and check if the time steps become tiny.