How to specify a 3 element column vector in Euler's Method for ODE
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Chris Horne
am 23 Mär. 2022
Beantwortet: Chris Horne
am 31 Mär. 2022
I am writing code that will approximate the solution to an ODE IVP. I want the initual condition to be a 3D column array supplied by the user rather than one number becuase I am simulating a 3D vector , u(t) that changes in time. I am unsure how to make this initial condition 3D vector.
% u'(t) = F(t, u(t)) where u(t) = t^3 + 12t^2- 20t +1
% u(0) = v % note v is a vector
% solve du/dt = t^3 + 12t^2- 20t + 1 using euler method
% Euler's Method
% Initial conditions and setup
h=input('Enter the step size') % step size
t=0:h:4;%(starting time value 0):h step size
%(the ending value of t3 ); % the range of t
u=zeros(size(t)); % allocate the result y
%v=input('Enter the intial vector of 3 components using brackets') ??????????
u(1,1,1)=v; % the initial u as 3D. I GET ERROR AT THIS LINE
n=numel(u); % the number of u values
% The loop to solve the ODE
for i = 1:n-1
dudt= *t(i).^3 +12*t(i).^2 -20*t(i)+1 ; %the expression for u' in the ODE
u(i+1) = u(i)+dudt*h ;
fprintf('="Y"\n\t %0.01f',u(i));
end
%%fprintf('="U"\n\t %0.01f',u);
plot(t,u);
xlabel('t')
ylabel('u(t)')
grid on;
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