Non linear equation containing integral
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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](https://www.mathworks.com/matlabcentral/answers/uploaded_files/222498/picture%201.png)
![picture 1.png](https://www.mathworks.com/matlabcentral/answers/uploaded_files/222498/picture%201.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)
댓글 수: 5
SACHIN VERMA
2020년 5월 29일
sir, i also got stuck in simlar problem, please help if anyone knows how to solve it for complicated functions like above...
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