Heun's method for Euler's solution

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Sachintha Alwis Weerasinghe 2017-3-23

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https://ww2.mathworks.cn/matlabcentral/answers/331517-heun-s-method-for-euler-s-solution

评论： Jan 2017-3-23

This code solves y'(t)=-2*y(t)+t with y(0)=1 using Euler method
% Initial Condition
y0 = 1;                  
h = 0.2;
% t goes from 0 to 3 seconds.
t = 0:h:3;              
% Preallocate array (good coding practice)
y_euler = zeros(size(t));  
% Initial condition gives solution at t=0.
y_euler(1) = y0;
% Solving the equation via Euler's method
for i=1:(length(t)-1)
    k1 = -2*y_euler(i)+t(i);  % Previous approx for y gives approx for derivative
    y_euler(i+1) = y_euler(i) + h*k1; % Approximate solution for next value of y
end