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Euler's Method
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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.
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回答(1 个)
Wan Ji
2021-8-22
编辑:Wan Ji
2021-8-23
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
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John D'Errico
2021-8-23
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.
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