MATLAB PROJECT

Time independent x and y variables was obtained in the following MATLAB code.

For the time interval t [0, 500] ms using the step sizes t = 20 ms and assume that y(0) = 0 for t = 0 s :

Write a MATLAB code to solve the ODE equation using the x and y values in the given code, using;

a) Euler Method

b) Modified Euler Method

(Hint: You can write the variable y(t) in the given ODE in terms of x(t). )

clc; T = readtable('info.dat'); T = table2array(T); y = T(:, 1); x = T(:, 2); logx = log(x);

p = polyfit(y, logx, 1); a = p(1); b = exp(p(2));

sum=0; for i=1:length(y) p=1; for j=1:length(y) if j~=i c = poly(y(j))/(y(i)-y(j)); p = conv(p,c); end end term = p*logx(i); sum= sum + term; end

info.dat

+4.60000E-01 +2.39944E-08 +5.00000E-01 +5.47030E-08 +9.70000E-01 +1.15987E-03 +1.21200E+00 +1.90309E-01 +1.24300E+00 +4.21568E-01

This MATLAB code solves the following equation.

dx(t) = [5 y(t) - 14x(t)] ODE dt x = b * (e)axy dx(t) = [5 y(t) - 14x(t)] ODE dt x = b * (e)axy