Question

MATLAB HELP .. SHOW CODE PLEASE

3. Stiff ODE The following second-order ODE is considered to be stiff. entre = -1001 - 1000.54 With ’ode45' command and the initial condition y(0) = 2 and y'(0) = 0, - Save the y(t) 0 <t<15) on HW8_4.dat file - Save the 0(t) (0 <t <15) on HW8_5.dat file

Answer 1

Matlab code for the problem

clc; clear; %Clear command window and workspace
t = [0 15]; %Time period
initial = [2 0]; % Initial condition
% The RHS of ODEs
f = @(t,y) [y(2); -1001*y(2)-1000.5*y(1)];
[t,y] = ode45(f,t,initial); %Computing the solution using ODE45 function
x = y(:,1); dx = y(:,2); % Copying the results to another variable for saving
save HW8_4.dat x -ascii
save HW8_5.dat dx -ascii
% For yor reference plotting the soltion y and derivative
plot(t,x), xlabel('t'), ylabel('y'); %Plotting the solution
figure
plot(t,dx), xlabel('t'), ylabel('dy/dt'); %Plotting the first derivative

Screen Print of the code

600 OWN clc; clear; %clear command window and workspace t = [O 15]; %Time period initial = [20]; % Initial condition % The RHS of ODES f = @(t,y) [y(2); -1001*y(2) - 1000.5*y(1)]; [t, y] = ode45(f, t, initial); %Computing the solution using ODE45 function x = y(:,1); dx = y(:,2); % Copying the results to another variable for saving save HW8_4.dat x -ascii save HW8_5.dat dx -ascii % For yor reference plotting the soltion y and derivative plot(t, x), xlabel('t'), ylabel('y'); %Plotting the solution figure plot(t, dx), xlabel('t'), ylabel('dy/dt'); %Plotting the first derivative 1 1 1
OUTPUT

The code will create two files HW8_4.dat and HW8_5.dat in the currwnt working directory

Figure 2 x Figure 1 x HW8_4.dat * CURRENT FOLDER Name GradeCalculate.m 1 HW8 4.dat !! HW8_5.dat Integralons Methods.m Jacobilteration.m 2 Number VarName2 Text VarName3 Text VarName4 Number N

| 15 10 2 mm mm 1 % % 8 0 y.

dy/dt