Warning: Failure at t=1.663240e-07. Unable to meet integration tolerances without reducing the step size below the smallest value allowed (4.235165e-22) at time t.

i am running this code ,

function file
function fn = plume5(t,Y)
global rho cp M R
 fn(1) =((-1/((rho(1)-(rho(1)*M)/R*Y(1))*(1/cp)))*(760.91-(1608.08*Y(1))+(2449.22*Y(1)^2)-(2001.61*Y(1)^3)+(904.51*Y(1)^4)-(212.087*Y(1)^5)+(20.095*Y(1)^6) ));
 fn(2) =((-1/((rho(2)-(rho(2)*M)/R*Y(1))*(1/cp)))*(760.91-(1608.08*Y(6))+(2449.22*Y(2)^2)-(2001.61*Y(2)^3)+(904.51*Y(2)^4)-(212.087*Y(2)^5)+(20.095*Y(2)^6) )); 
 fn(3)= ((-1/((rho(3)-(rho(3)*M)/R*Y(1))*(1/cp)))*(760.91-(1608.08*Y(7))+(2449.22*Y(3)^2)-(2001.61*Y(3)^3)+(904.51*Y(3)^4)-(212.087*Y(3)^5)+(20.095*Y(3)^6)));
 fn(4)= ((-1/((rho(4)-(rho(4)*M)/R*Y(1))*(1/cp)))*(760.91-(1608.08*Y(8))+(2449.22*Y(4)^2)-(2001.61*Y(4)^3)+(904.51*Y(4)^4)-(212.087*Y(4)^5)+(20.095*Y(4)^6)));
 fn(5) = (-1/(rho(5)*Y(5)))*(1.113-2.14*Y(5)+2.81*Y(5)^2-1.76*Y(5)^3+0.396*Y(5)^4+0.08694*Y(5)^5-0.0579*Y(5)^6 +0.0077*Y(5)^7);
 fn(6) = (-1/(rho(6)*Y(6)))*(1.113-2.14*Y(6)+2.81*Y(6)^2-1.76*Y(6)^3+0.396*Y(6)^4+0.08694*Y(6)^5-0.0579*Y(6)^6 +0.0077*Y(6)^7);
 fn(7) = (-1/(rho(7)*Y(7)))*(1.113-2.14*Y(7)+2.81*Y(7)^2-1.76*Y(7)^3+0.396*Y(7)^4+0.08694*Y(7)^5-0.0579*Y(7)^6 +0.0077*Y(7)^7);
 fn(8) = (-1/(rho(8)*Y(8)))*(1.113-2.14*Y(8)+2.81*Y(8)^2-1.76*Y(8)^3+0.396*Y(8)^4+0.08694*Y(8)^5-0.0579*Y(8)^6 +0.0077*Y(8)^7);
fn = fn';

main file

clear all
close all
global rho cp M R  
l = 2.8919
rho = [0.4586;0.7860;1.1449;1.1611;0.4586;0.7860;1.1449;1.1611]
x_CO2 = 0.5;
x_H2O = 0.5;
R = 8.314;      %m3.Pa/mol/K
cp_CO2 = 1168;      %J/kg/K
cp_H2O = 2147;      %J/kg/K
cp = (x_CO2*cp_CO2)+(x_H2O*cp_H2O);
M_CO2 = 44*(10^-3);          %kg/mol
M_H2O = 18*(10^-3);          %kg/mol
M = (x_CO2*M_CO2) + (x_H2O*M_H2O);
t_span= 0:0.01:0.05
y = [0.0182;0.3105;1.2882;2.7341;0.0182;0.3105;1.2882;2.7341]
[A,P]= ode45('plume5',t_span,y);

but it states that its unable to meet the integration tolerances,without reducing the step size below the smallest value allowed (4.235165e-22) at time t.

[Jayanth Bhimavarapu]

Hi Sunetra

Try to relax the tolerance using odeset and then execute your script again.

>> my_opt = odeset('AbsTol',1E-5);

For more details refer:

https://www.mathworks.com/help/matlab/ref/odeset.html#namevaluepairarguments

However the value of tolerance depends on your data.

And pass this as an argument to your ode45 function as:

>> [A,P]= ode45('plume5',t_span,y,my_opt);

For more details refer:https://www.mathworks.com/help/matlab/ref/ode45.html#bu00_4l_sep_shared-options

Thanks

Jayanth