I am not sure why you wrote the function firstorderDSC1 like that, but reviewing it briefly, it appears that the ode function you have written inside it to fit the data is wrong. Check the differences of your code with this code
clc
clear all;
close all;
%xdata
T = 294:0.1:361;
T=T';
%ydata
for i=1:size(T,1)
f1(i)= 0.2099*exp(-((T(i)-340.2)/2.439).^2);
end
f1=f1';
%Initial value for unknown coefficient
B0 =rand(1,3);
%find the local fit using lsqcurvefit
options = optimoptions('lsqcurvefit','FiniteDifferenceType','central','OptimalityTolerance',1e-12,'FunctionTolerance',1e-12, 'MaxFunctionEvaluations',1500);
lb = [-Inf];
ub = [Inf];
[B,Rsdnrm,Rsd,ExFlg,OptmInfo,Lmda,Jmat] = lsqcurvefit(@firstorderDSC1,B0,T,f1,lb,ub,options);
% Set up the problem for MultiStart
problem = createOptimProblem('lsqcurvefit','x0',B0,'objective',@firstorderDSC1,...
'lb',lb,'ub',ub,'xdata',T,'ydata',f1);
ms = MultiStart('PlotFcns',@gsplotbestf);
[xmulti,errormulti] = run(ms,problem,50);
%plot the result
figure;
plot(T,f1,T,firstorderDSC1(xmulti,T),'LineWidth',3)
legend('Data','Fitted result')
function dndt2 = firstorderDSC1(B, T)
%my differential equation
function denaturate = firstorderDSC(T, n)
a= (exp(183.8)./1.5); %(1/s)
dndT=B(1)*exp(-((T-B(2))/B(3)).^2);
denaturate=dndT;
end
%solving my differential equation
options = odeset('AbsTol', 1e-8,'RelTol',1e-8);%,'OutputFcn',@odeplot);
[temp,num] = ode23s(@firstorderDSC, T, 0, options);
dndt2 = firstorderDSC(temp,num);
end
Both lines overlap.
