Question

Problem 9 Consider the following system of equations dr eds. dt 6y2 Use Euler's Method on this system starting at (xo,yo) (1,1) with Δ-025 and n-6.

Answer 1

MATLAB Code:

close all
clear
clc

delta_t = 0.25; n = 6;
x(1) = 1; y(1) = 1; % Initial values

fprintf('%-5s\t%-10s\t%-10s\n', 'Step', 'x', 'y')
fprintf('%-5d\t%-10.4f\t%-10.4f\n', 0, x(1), y(1))
for i=1:n
mx = dxdt(y(i));
my = dydt(x(i), y(i));
x(i + 1) = x(i) + delta_t*mx; % Euler
y(i + 1) = y(i) + delta_t*my; % Update
fprintf('%-5d\t%-10.4f\t%-10.4f\n', i, x(i + 1), y(i + 1))
end

function out = dxdt(y)
out = y + y^2;
end

function out = dydt(x,y)
out = -x + y/5 - x*y + 6*(y^2)/5;
end

Output Screenshot:

Command Window Step x 1.8888 1.5e00 1.8931 2.8482 2.8838 1.9429 1.892 1.8888 69·棠淋69 -0.1819 -e.5983 8.7228 0.7367 8