project1_skeleton_1

School

University of Central Florida *

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Course

3034C

Subject

Aerospace Engineering

Date

Oct 30, 2023

Type

Pages

Uploaded by MagistrateNeutronAlpaca26

% NAME: % DATE: 09/08/23 % ASSN: PROJECT 1 % CSRN: EML 3034C Modeling Methods in MAE % Clear command window, close all graphs, clear workspace clc, close all, clear % ======================================================================== fprintf("============================================================\n") fprintf("Project 1 - Round-off vs Truncation Error\n") fprintf("\n") display(date()) fprintf("============================================================\n\n") % ======================================================================== format short e % Define the function f(x) f = @(x) 2.5-1.25.*cos(3.8.*x); % Insert Function f(x) df = @(x) 4.75.*sin(3.8.*x); % Insert Exact First Derivative df(x) % Select x value to evaluate derivative x = 5.25; % Double-Precision % loop through the exponents for each delta x value and evaluate the derivative for i = 1:20 % calculate the delta x del(i,1) = 10^(-i); % Backward Finite Difference backward(i,1) = (f(x)-f(x-del(i,1)))/del(i,1); % Forward Finite Difference forward(i,1) = (f(x+del(i,1))-f(x))/del(i,1); % Central Finite Difference central(i,1) = (f(x+del(i,1))-f(x-del(i,1)))/(2.*del(i,1)); % calculate the errors compared to exact (analytical) derivative backward_error(i,1) = abs(df(x)-backward(i,1)); forward_error(i,1) = abs(df(x)-forward(i,1)); central_error(i,1) = abs(df(x)-central(i,1)); end % Plot the error vs del x for each method on the log scale figure(1) hold on % Scale of log for axis set(gca, 'XScale', 'log', 'YScale', 'log') % the loglog() function is the same as plot() but on log scale for both axes loglog(del,backward_error) loglog(del,forward_error) loglog(del,central_error)

xlabel('\Delta'), ylabel('Error') title('Error on Forward, Backward, and Central') legend('Forward','Backward','Central') grid on, hold off % assemble the results into a table (actually a matrix) Table = [del forward_error backward_error central_error]; % print to screen fprintf("=========== Double Precision Results ===========\n") disp(Table) % Repeat everything, but in single precision % Select x value to evaluate derivative x = single(5.25); for i = single(1:20) % calculate the delta x del(i,1) = 10^(-i); % Backward Finite Difference backward(i,1) = (single(f(x))-single(f(x-del(i,1))))/single(del(i,1)); % Forward Finite Difference forward(i,1) = (single(f(x+del(i,1)))-single(f(x)))/single(del(i,1)); % Central Finite Difference central(i,1) = (single(f(x+del(i,1)))-single(f(x-del(i,1))))/ (2.*single(del(i,1))); % calculate the errors compared to exact (analytical) derivative backward_error(i,1) = abs(single(df(x))-backward(i,1)); forward_error(i,1) = abs(single(df(x))-forward(i,1)); central_error(i,1) = abs(single(df(x))-central(i,1)); end % Plot the error vs del x for each method on the log scale figure hold on % Scale of log for axis set(gca, 'XScale', 'log', 'YScale', 'log') % the loglog() function is the same as plot() but on log scale for both axes loglog(del,backward_error) loglog(del,forward_error) loglog(del,central_error) xlabel('\Delta'), ylabel('Error') title('Error on Forward, Backward, and Central') legend('Forward','Backward','Central') grid on % assemble the results into a table (actually a matrix) fprintf("\n\n\n\n\n")

Table = [del forward_error backward_error central_error]; % print to screen fprintf("=========== Single Precision Results ===========\n") disp(Table); fprintf("\n\n\n\n\n\n\n") %ADDED TO MAKE IT PRINT MORE LEGIBLY WHEN PUBLISHED AS PDF

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