# I want to find unknown value for nonlinear equation.

1 view (last 30 days)
M.Rameswari Sudha on 14 Mar 2022
Commented: M.Rameswari Sudha on 16 Mar 2022
I want to find t1 value by search method with mesh grid plot between t1 and TC. Anyone help me to do this problem.
function tcfun()
clc
close all
t1=0:0.5:3;
TC=f(t1);
r0=[0.20;10];
alfa=0.2;
while abs (f(r0(1))) > 1e-2
r0 = r0 - alfa.*(f(r0(1)))./fprime(r0(1));
end
hold on
r0=[0.1]
alfa=0.2;
for index = 1:100
r0 = r0 - alfa.*inv(fdb1prime(r0(1)).*fprime(r0(1)));
end
r0
f(r0(1))
plot(r0(1),f(r0(1)),'rs','Markersize',20)
function TC = f(t1)
A0 =500;
D0=100;
c1=5;
c2=10;
c3=10;
c4=8;
a=30;
a2=40;
m=0.5;
b=5;
b2=7;
mu1=4;
mu2=8;
T=12;
k1=0.01;
k0=0.03;
TC=(1./T).*(A0+c1.*((b-a).*t1-(b.*t1^2./2)+(a+b.*(1+m)).*log((1+m-t1)./(1+m)))+c2.*((b.*t1^2./2)+(a+b.*(1+m)).*(t1+(1+m).*log(1+m-t1)))+c3.*((a./k1)-(b.*(1-k1.*T)./k1^2).*(mu1.*(log((1+k1.*(mu1-T))./(1+k1.*(t1-T)))-1)+t1)+((1-k1.*T)./k1).*(log((1+k1.*(mu1-T))./(1+k1.*(t1-T))))+(b.*k0./2.*k1).*(mu1-t1).^2+((a./k1)-(b.*k0.*(1-k1.*T)./k1^2).*(log((1+k1.*(mu1-T))./(1+k1.*(t1-T)))).*(mu2-mu1)+(k0.*D0./k1).*(mu2.*(log((1+k1.*(mu2-T))./(1+k1.*(t1-T)))-1)-mu1.*(log((1+k1.*(mu1-T))./(1+k1.*(t1-T)))-1)+((1-k1.*T)./k1).*(log((1+k1.*(mu2-T))./(1+k1.*(mu1-T))))+((a./k1)-(b.*k0.*(1-k1.*T)./k1^2).*(log((1+k1.*(mu1-T))./(1+k1.*(t1-T)))).*(T-mu2)+(b.*k0./k1).*(mu1-t1).*(T-mu2)+(k0.*D0./k1).*(log((1+k1.*(mu2-T))./(1+k1.*(mu1-T)))).*(T-mu2)-(k0.*b2./2.*k1).*(mu2-T).^2+((1./k1)-T)+(T-(1./k1)).*(T.*(log(1+k1(t1-T))-1)-mu2.*(log((1+k1.*(mu2-T))./(1+k1.*(t1-T)))-1))+(T-(1./k1)).*log(1+k1.*(mu2-T))))+c4.*(a.*(mu1-t1)+(b2./2).*(mu1.^2-t1.^2)-k0.*(a./k1)-(b.*(1-k1.*T)./k1^2).*(log((1+k1.*(mu1-T))./(1+k1.*(t1-T))))+(b./k1).*(mu1-t1))+D0.*(mu2-mu1)-(D0.*k0./k1).*(log((1+k1.*(mu2-T))./(1+k1.*(mu1-T))))+(1./2.*b2).*((a2-b2.*mu2).^2-(a2-b2.*T).^2)+k0.*a2.*log(1+k1.*(mu2-T))-(b2./k1).*(T-mu2)+(b2./k1).*(T-(1./k1)).*log(1+k1.*(mu2-T)))));
function TCprime = fprime(t1)
dfdt1=(1./T).*(c1.*((b-a)-b.*t1-((a+b.*(1+m))./(1+m-t1)))+c2.*(b.*t1-((a+b.*(1+m).*t1)./(1+m-t1)))+c3.*((a./k1)-(b.*(1-k1.*T)./k1^2).*(((-mu1.*k1)./(1+k1.*(t1-T)))+1)-((1-k1.*T)./(1+k1.*(t1-T)))+((b.*k0.*(t1-mu1))./k1)-((a-b.*k0.*(1-k1.*T))./k1).*((mu2-mu1)./(1+k1.*(t1-T)))+(k0.*D0./k1).*((k1.*(mu1-mu2)./(1+k1.*(t1-T)))-(a-((b.*k0.*(1-k1.*T))./k1)).*((T-k2)./(1+k1.*(t1-T)))+(b.*k0.*(mu2-T)./k1)-(1-k1.*T).*((T+mu2)./(1+k1.*(t1-T)))))+c4.*(-a2+b2.*t1+k0.*((a-b.*(1-k1.*T))./k1).*(1./(1+k1.*(t1-T)))+(b./k1)));
end
end
end
mesh(t1,TC)
Torsten on 15 Mar 2022
I got the answer. But I need feasible solution. so , I want to apply optimization by using any one of search method.
But how can you be sure your method gives a feasible solution ?
As shown by the symbolic computation, there are three solutions for t1. Your Newton method will converge to any of them depending on the starting guess you choose for t1.
M.Rameswari Sudha on 16 Mar 2022
Yes, You are correct. I misunderstood the method of finding the solution. Thank you for providing the right suggestion. Thank you.

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