Question

MATLAB

(2 points) Challenge. Create a SCRIPT file called thirdOrderDE.m 5) Blasius showed in 1908 that the solution to the incompressible flow field in a laminar boundary layer on a flat plate is given by the solution of the fol- lowing third-order ordinary nonlinear differential equation Rewrite this equation into a system of three first-order equations, using the following substitutions: h,(m) = f d2 Solve using the ode45 function with the following initial conditions: hi (0) = 0 hs(0) = 0.332 for η = 0 to 1 Plot all three curves on the same plot and save as thirdOrderDE.jpg

Answer 1

Matlab Code:

clear;clc;
init = [0 0 0.332];%initial conditions
tspan = 0:0.01:1;

[t, y] = ode45(@thODE, tspan, init);%function call to solve

%plots
plot(t,y(:,1));
hold on;
plot(t,y(:,2));
hold on;
plot(t,y(:,3));
hold on;
legend('f','deriv(f)','doublederiv(f)');

%differential equations
function dydt = thODE(t,y)
dydt = zeros(3,1);
dydt(1) = y(2);
dydt(2) = y(3);
dydt(3) = (-1/2)*y(1)*y(3);
  
end

0.35 deriv(f) 0.3 doublederiv(f) 0.25 0.2 0.15 0.1 0.05 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.91