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%-----------------------------------------------------------------
% clear;
% ts = 0; % set initial value of x_0
% is = 0;
% h = 0.0001; % set step-size
% tf = 0.03; % stop here
% R = 0.5;
% L = 0.0015;
%
% A = 6;
% T = 0.00015;
%
% vin = @(t) A * cos(2*pi*t/T);
% func = @(t, iout) (vin(t) - iout*R) / L; % define func
% [t, iout ] = midpoint(func, ts, tf, is, h);
%
% %numerical solution
% vout = vin(t) - iout * R;
%
% %obtaining the exact solution with favorite method
% i_Exact = (6/L)*((2*pi)/T * sin((2*pi)/T*t) + (R/L)*cos((2*pi)/T*t) - (R/L)*exp(-(R/L)*t))/((2*pi)/T^2 + (R/L)^2);
% exact = vin(t) - R*i_Exact;
%
% %error as a function of t
% error = exact - vout;
%
% figure(2);
% plot(t,error); %for midpoint
% figure(3);
% t = logspace(-10 ,1);
% loglog(t,error);
% grid on;
%--------------------------------------------------------------------
clear;
ts = 0; % set initial value of x_0
is = 0;
h = 0.0000005; % set step-size
tf = 0.03; % stop here
R = 0.5;
L = 0.0015;
A = 6;
T = 0.00015;
vin = @(t) A * cos(2*pi*t/T);
func = @(t, iout) (vin(t) - iout*R) / L; % define func
[t, iout ] = ralston(func, ts, tf, is, h);
%numerical solution
vout = vin(t) - iout * R;
%obtaining the exact solution with favorite method
i_Exact = @(t) (6/L)*((2*pi)/T * sin((2*pi)/T*t) + (R/L)*cos((2*pi)/T*t) - (R/L)*exp(-(R/L)*t))/((2*pi)/T^2 + (R/L)^2);
exact = vin(t) - R*i_Exact(t);
%error as a function of t
error = abs(exact - vout);
figure(3);
plot(t,error); %for ralston
max_error = max(error);
figure(5);
for k = 1:5
[t, iout] = ralston(func, ts, tf, is, h);
exact = vin(t) - R*i_Exact;
vout = vin(t) - R*iout;
error = abs(exact - vout);
max_error = max(error);
plot(log(t), log(max_error),'b*');
hold on;
h = 2*h;
end
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