Forward Euler oscillations in plot

Question

Arkajyoti Chaterjee 2021-1-11

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/714133-forward-euler-oscillations-in-plot

回答： Aashray 2025-6-26

The following code ought to apply the Forward/Explicit Euler method to solve the ODE and plot a graph. However it displays oscillations.

clc
syms t
S = solve((10 - (10+t)*exp(-t)) + 10*exp(-200*t) == 10, t);                       % Solve to get start of domain.
h = 0.01;                                                                         % Step Size.
x = S:h:S+10;                                                                     % Take a domain of 10 and divide into steps.
z = zeros(1,length(x));                                                           % Pre-allocate.
z(1) = 10;                                                                        % Initial Condition.
Y = @(t,r) -200*(r - (10 - (10+t)*exp(-t))) + exp(-t)*(9 + t);                    % Function.
for i=1:(length(x)-1)                                                             % Iteration loop. 
      y(i+1) = y(i) + h * Y(x(i),y(i));                                           % https://en.wikipedia.org/wiki/Euler_method#Informal_geometrical_description
end
plot(x,y,'-or','DisplayName','FE-code approximation');