I want to find unknown value for nonlinear equation.

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M.Rameswari Sudha 2022-3-14

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1670974-i-want-to-find-unknown-value-for-nonlinear-equation

评论： M.Rameswari Sudha 2022-3-16

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)

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Torsten 2022-3-15

@M.Rameswari Sudha

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 2022-3-16