The code doesn't work....

hello everyone

I am practicing numerical differentiation. However, the numerical analysis values ​​and actual values ​​do not appear on the graph at the same time and seem to conflict. Where did we go wrong? Thank you for reading this long sentence. have a good day:)

here is my code :

clc; clear all; close all;
fun = @(t) -0.01953125.*t.^2 + 18.75.*t
est_point = 100;
da = 1;

dfda_central = (fun(est_point + da) - fun(est_point - da))./2*da
x = 0:0.01:960;
fx = fun(x);
dfda_true = -0.0390625.*est_point + 18.75

dgraph = @(point, dfda, t) dfda*t + (fun(point) - dfda*point);


figure(1)
plot(x,fx,'black','linewidth',2); hold on;
plot(x, dgraph(est_point, dfda_central, x),'red'); hold on;
plot(x, dfda_true,'blue'); hold on;
grid on;

rel_error=norm(dfda_true-dfda_central)/norm(dfda_true);
disp(rel_error);
disp(dfda_true);

Answer 1

[Hassaan]

clc; clear all; close all;

% Define the function
fun = @(t) -0.01953125.*t.^2 + 18.75.*t;

% Estimation point and step size
est_point = 100;
da = 1;

% Central difference calculation
dfda_central = (fun(est_point + da) - fun(est_point - da)) / (2*da);

% Define the range and function values for plotting
x = 0:0.01:960;
fx = fun(x);

% True derivative value
dfda_true = -0.0390625.*est_point + 18.75;

% Define the line representing the central difference derivative
dgraph = @(point, dfda, t) dfda * t + (fun(point) - dfda * point);

% Plot the original function
figure(1);
plot(x, fx, 'black', 'linewidth', 2); hold on;

% Plot the central difference approximation
plot(x, dgraph(est_point, dfda_central, x), 'red');

% Plot the true derivative as a constant line
plot(x, dfda_true * ones(size(x)), 'blue');

% Add grid and legend
grid on;
legend('Function', 'Central Difference Approximation', 'True Derivative');

% Calculate and display the relative error
rel_error = norm(dfda_true - dfda_central) / norm(dfda_true);
disp(['Relative Error: ', num2str(rel_error)]);

Relative Error: 0

disp(['True Derivative: ', num2str(dfda_true)]);

True Derivative: 14.8438

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