while loop convergence criteria

im writing a program to compute the definite integral of a function over a given interval using the midpoint rule. i have the program doing what i want but instead of just looping 1000 times to get a fairly accurate answer i want it to loop until the answer is increasing by less than .0001 im having trouble implementing that criteria.

heres my code so far

clc
clear
f = input('Gimme the function: ', 's');
f = str2func (['@(x)' f]);
n = 0;
a = input('lower bound ');
b = input('upper bound ');
while n<=1000
    n=n+1;
    delta = (b-a)/n;
    x = a + delta*(1:2:2*n-1)/2;
    m = delta*sum(f(x));
end
disp(['The integral is ' num2str(m

Answer 1

[Walter Roberson]

Before the loop,

old_fx = infinity;
new_fx = -infinity;

Change the loop condition to

while abs(old_fx - new_fx) > 0.0001

And just inside the loop finishing:

old_fx = new_fx;
new_fx = f(x);

[GreGG]

thank you that worked perfect

Answer 2

[Rajeev Upadhyay]

I need to resolve the convergence issue with While loop. Please suggest what should I do to run the program.

T_Res=582.0;

Molecular_Weight=16.64035;

Molecular_Wt_Air=28.97;

Gas_Gravity=Molecular_Weight/Molecular_Wt_Air;

K1=(0.00094+0.000002*Molecular_Weight)*(T_Res^1.5)/(200+19*Molecular_Weight+T_Res);

X=3.5+(986/T_Res)+(0.01*Molecular_Weight);

Y=2.4-0.2*X;

Sp_gr_oil=0.85;

Sp_gr_gas=0.6;

API_gr=(141.5/Sp_gr_oil)-131.5;

a=0.0125*API_gr-0.00091*(T_Res-460);

% for Z Calculation

T_crit=341.8116;

t=T_crit/T_Res;

P_crit=666.541;

E=0.06125*t*exp(-1.2*(1-t)^2)/P_crit;

% Dead Oil Viscosity

Z=3.0324-0.02023*Sp_gr_oil;

y=10^Z;

X=y*T_Res^(-1.163);

Dead_Oil_Viscosity=10^X-1;

% For Rel_Perm

Swcon=0.3;

Sorg=0.2;

Sgcon=0.05;

Krogcg=0.8;

Krgcl=0.9;

nog=2;

ng=2;

N=100;

P=3550;

GOR=0;

Np=0;

Gp=0;

Delta_P=50;

nstep=70;

Rsi=Sp_gr_gas*(((P/18.2)+1.4)*10^a);

Boi=0.9759+0.00012*((Rsi*(Sp_gr_gas/Sp_gr_oil)^0.5)+(1.25*(T_Res-460)))^1.2;

results=zeros(nstep,12);

f=inline('-E*P+((x+x^2+x^3-x^4)/(1-x)^3)-((14.76*t-9.76*t^2+4.58*t^3)*x^2)+((90.7*t-242.2*t^2+42.4*t^3)*x^(2.18+2.82*t))');

syms x

g=inline(diff(f(E,P,t,x)));

for i=1:nstep

P=P-Delta_P;

Rs=Sp_gr_gas*(((P/18.2)+1.4)*10^a);

Bo=0.9759+0.00012*((Rs*(Sp_gr_gas/Sp_gr_oil)^0.5)+(1.25*(T_Res-460)))^1.2;

A=10.715*(Rs+100)^(-0.515);

B=5.44*(Rs+150)^(-0.338);

Oil_Viscosity=A*Dead_Oil_Viscosity^B;

Gas_Density=0.00149406*P*Molecular_Weight/Z/T_Res;

Gas_Viscosity=K1*exp(X*Gas_Density^Y);

x=0.1;

while abs(f(E,P,t,x))>1e-05

x1=x-f(E,P,t,x)/g(x);

x=x1;

end

z=E*P/x;

Bg=0.00503676*z*T_Res/P;

m=0.1;

Np1=(N*m-Np);

Np=Np+Np1;

Gp1=(N*((Bo-Boi)+(Rsi-Rs)*Bg)-Np*(Bo-Rs*Bg))/Bg;

So=(1-Swcon)*(1-m)*Bo/Boi;

Sl=So+Swcon;

if Sl<(Sorg+Swcon)

Krog=0;

Krg=Krgcl;

elseif Sl>=(1-Sgcon);

Krog=Krogcg;

Krg=0;

else Krg=Krgcl*((1-Sl-Sgcon)/(1-Sgcon-Sorg-Swcon))^ng;

Krog=Krogcg*((Sl-Sorg-Swcon)/(1-Sgcon-Sorg-Swcon))^nog;

end

Ratio_Rel_Perm=Krg/Krog;

GOR1=Rs+(Ratio_Rel_Perm*Oil_Viscosity*Bo/Gas_Viscosity/Bg);

GOR_Avg=(GOR1+GOR)/2;

GOR=GOR_Avg;

Gp2=Gp+(GOR*Np1);

u=inline('((N*((Bo-Boi)+(Rsi-Rs)*Bg)-m*N*(Bo-Rs*Bg))/Bg)-(Gp+(GOR*Np1))')

syms m

v=inline(diff(u(Bg,Bo,Boi,GOR,Gp,m,N,Np1,Rs,Rsi)))

m=0.1;

while abs(u(Bg,Bo,Boi,GOR,Gp,N,Np1,Rs,Rsi,m))>0.5

m1=m-u(Bg,Bo,Boi,GOR,Gp,N,Np1,Rs,Rsi,m)/v(m);

m=m1;

end

Np=N*m;

Gp=(N*((Bo-Boi)+(Rsi-Rs)*Bg)-Np*(Bo-Rs*Bg))/Bg;

results(i,1)=P;

results(i,2)=Rs;

results(i,3)=Bo;

results(i,4)=Oil_Viscosity;

results(i,5)=Gas_Viscosity;

results(i,6)=Bg;

results(i,7)=Sl;

results(i,8)=Ratio_Rel_Perm;

results(i,9)=GOR;

results(i,10)=Np;

results(i,11)=Gp;

results(i,12)=m;

end

plotyy(results(:,1),results(:,2),results(:,1),results(:,3))

plot(results(:,1),results(:,10))