Solve IVP with modified Euler's method

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Kevin Mekulu
Kevin Mekulu 2017-11-13
回答： My Anh Vu 2023-4-1
I am trying to solve the initial value problem x'(t) = t/(1+x^2) with x(0) = 0 and 0 <= t <= 5 using modified Euler's method with 10 steps however I am not too sure about my code can anyone double check/provide a more efficient code? thanks in advance
function [T,Y] = euler_modified(f,a,b,ya,m)
h = (b - a)/m;
T = zeros(1,m+1);
Y = zeros(1,m+1);
T(1) = a;
Y(1) = ya;
for j=1:m,
Y(j+1) = Y(j) + h*feval(f,T(j) + h/2,Y(j) + h*feval(f,T(j),Y(j)));
T(j+1) = a + h*j;
end
  1 个评论
John D'Errico
John D'Errico 2017-11-13
Why do you care if the code is not as efficient as you wish? This is homework, as otherwise, you would not want to use Euler's method in any form. If not homework, then there are batter methods to solve an ODE, and they are already written. NEVER write code when professionally written code is given to you as part of the language itself.

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回答（2 个）

ali alnashri
ali alnashri 2021-4-14
function [T,Y] = euler_modified(f,a,b,ya,m)
h = (b - a)/m;
T = zeros(1,m+1);
Y = zeros(1,m+1);
T(1) = a;
Y(1) = ya;
for j=1:m,
Y(j+1) = Y(j) + h*feval(f,T(j) + h/2,Y(j) + h*feval(f,T(j),Y(j)));
T(j+1) = a + h*j;
end
My Anh Vu
My Anh Vu 2023-4-1
Y(j+1) = Y(j) + h*feval(f,T(j) + h/2,Y(j) + h*feval(f,T(j),Y(j)));
should be Y(j+1) = Y(j) + h*feval(f,T(j) + h/2,Y(j) + h/2*feval(f,T(j),Y(j)));
Good luck!

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