I want to find unknown value for nonlinear equation.

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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)
  7 Comments
M.Rameswari Sudha
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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