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
