Unable to meet integration tolerances without reducing the step size problem.

Hello Everyone.

I am facing 'Warning: Failure at t=0.000000e+00. Unable to meet integration tolerances without reducing the step size below the smallest value allowed (7.905050e-323) at time t, error for the following code. How can I fix it.

clc
clear all

A =1.4036e-18;
B = 3.4302e-18;
e=1.60217663e-19;
T_e=3; 

f = @(t,x) [(sqrt(A/x(1)))*(-x(4)-(0.424)+(1.6977)*exp(-(e/T_e)*(x(1))));
           (sqrt(A/x(1)))*(x(4)-(0.663)+(2.6540)*exp(-(e/T_e)*(x(2))));
           -(2.994*10^5)*x(4);
           ((x(1))-(x(2))+x(3)+60*(cos(t)))-2.55*10^7*x(4)];
       
[t,xa] = ode15s(f,[0, 80],[0,0,-62,0]);

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

Answer 1

[Torsten]

You define an initial condition for x(1) as 0, but you divide by x(1) in equations 1 and 2.

This won't work.

[Steven Lord]

Yes. Evaluating the ODE function at the initial conditions:

A =1.4036e-18;
B = 3.4302e-18;
e=1.60217663e-19;
T_e=3; 
f = @(t,x) [(sqrt(A/x(1)))*(-x(4)-(0.424)+(1.6977)*exp(-(e/T_e)*(x(1))));
           (sqrt(A/x(1)))*(x(4)-(0.663)+(2.6540)*exp(-(e/T_e)*(x(2))));
           -(2.994*10^5)*x(4);
           ((x(1))-(x(2))+x(3)+60*(cos(t)))-2.55*10^7*x(4)];
init = f(0, [0,0,-62,0])

init = 4×1

Inf Inf 0 -2

A function with an infinite rate of change at the initial point seems like a Bad Thing.

[Md. Golam Zakaria]

@Steven Lord, If I chose nonzero initial conditions will it solve my problem. I didnt do it because It takes too much time to solve

[Torsten]

If I chose nonzero initial conditions will it solve my problem.

Nobody knows. Just try it.