Non linear equation containing integral

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Anil Kumar 2019-6-3

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/465290-non-linear-equation-containing-integral

评论： SACHIN VERMA 2020-5-29

I am bit new with matlab programming. I want to solve the above equation for phi0 but getting problem using solve function. Please help me. I expect a solution like this: different phi0 for different Nt picture 1.png

clc;clear;close all;
warning('off')
% number of data points for r, R and Et-Ef
N = 100;
% define the parameters
Nd = 1e24;
e  = 12*1e-12;
r  = 40*1e-9
R  = 40*1e-9;
Et_Ef = 0.21*1.6*1e-19;
K  = 1.3807e-23;
T  = 600;
Nt = 1e11;
q  = 1.6e-19;
for j = 1:length(Nt)
% initializing
LHS_vals = [];
RHS_vals = [];
P = [];
% loop to solve LHS - RHS = 0 N times
for i = 1:N
    
    syms phi0
    
    Ld = sqrt(e*K*T/(q^2*Nd));
    integrand = @(r)Nd-(Nd.*exp(-1.*(phi0+(1./6).*(r(i)/Ld).^2)));
    LHS = integral (integrand,0,40*10^-9);
    RHS = 4.*pi.*R.^2.*Nt./(1+2.*exp(Et_Ef + K.*T .*(phi0 + (1/6).*(r(i)./Ld).^2)));
    eq =  LHS - RHS==0;
    
    phi0 = solve(eq,phi0)
    
    if ~isempty(phi0)
        
    LHS_vals(end+1) = eval(LHS);
    RHS_vals(end+1) = eval(RHS);
    P(end+1) = phi0;
    
    fprintf('LHS - RHS = %1.2e\n',eval(LHS) - eval(RHS))
    end
    
end
%Plotting the Figure
if ~isempty(P)
    
figure()
hold on
plot(P,RHS_vals,'r--')
plot(P,LHS_vals,'b--')
hold off
xlabel('\phi_0')
ylabel('LHS,RHS')
ax = gca;
ax.YScale = 'log';
legend('RHS','LHS')
end
end
%plot (r,phi0)