Euler's Method

Hello,

𝑑𝑦/𝑑𝑥 = 𝑥^-2 (𝑆𝑖𝑛2𝑥−2𝑥𝑦), 𝑦(1)=2

I need to write code to calculate the values of y(x) when 1≤𝑥≤2 and h=0.25 by using Euler's Method.

But I couldn't take the integral of dy/dx which I will use for my code. To solve integral, I used integration by parts but the answer didn't come. I dont know can I write directly in Matlab code or not. Can you please help me? I really need help.

Answer 1

[Wan Ji]

Euler forward?

clc;clear
odefun = @(x,y) x^(-2) *(sin(2*x)-2*x*y); % I have rewritten the ode function
xspan = [1,2];
x0 = xspan(1);
y0 = 2;
h = 0.25;
nstep = diff(xspan)/h;
obj = ode(odefun, x0, y0);
a = obj.forwardEuler(h, nstep);
plot(a.t, a.y)
xlabel('x'); ylabel('y')

the ode class

classdef ode
    properties
        odefun
        t0
        y0
        t
        y
    end
    methods
        function obj = ode(odefun, t0, y0)
            obj.odefun = odefun;
            obj.t0 = t0;
            obj.y0 = y0;
        end
        function obj = forwardEuler(obj, dt, nstep)
            obj.t = obj.t0 + (0:nstep)*dt;
            obj.y = zeros(numel(obj.y0), numel(obj.t));
            obj.y(:,1) = obj.y0;
            for i = 1:1:nstep
                obj.y(:,i+1) = obj.y(:,i) + dt*obj.odefun(obj.t(i),obj.y(:,i));
            end
        end
    end
end

[John D'Errico]

Please don't do student;s homework assignments for them. This does not help the student, except to learn there will be someone willing to do their job for them, if only they ask. And that does more to hurt the student than to help them. It also damages the site itself, since by encouraging students to post their homework with no effort shown or made, they will do it again.

[Wan Ji]

@Ahmet Akcura Oui, d'accord!@John D'Errico