Error in ODE 45: MYODE must return a column vector.

I am trying to discretize a system of PDEs with a finite difference scheme and solve the resulting ODE system with ODE45:

PDE Solver code:

global N;global dx;

global a11; global a12; global a22; global a21;

a11=1;a12=1; a22=1;a21=1;

dx = .05;

X = -2:dx:2;

N = length(X);

tspan = [0 2];

u = ones(1,N);

v = 2*ones(1,N);

%Initial Data

%%

y0 = [u,v];

%%

% Solve ODE

[t,y] = ode45(@myODE, tspan, y0);

myODE code:

function dy = myODE(~,y)

global N;

global dx;

global a11; global a12; global a22; global a21;

u=y(1:N);

v = y((N+1):2*N);

du = zeros(size(u));

dv = zeros(size(v));

du(1) = (2*a11*(u(2)-u(1)))/(dx^2)+a12*(u(1)*v(2)-u(2)*v(1)-u(1)*v(1)-u(2)*v(2))/(dx^2);

dv(1) = 2*a22*(v(2)-v(1))/(dx^2)+a21*(v(1)*u(2)-v(2)*u(1)-v(1)*u(1)-v(2)*u(2))/(dx^2);

du(N) = 2*a11*(u(N-1)-u(N))/(dx^2)+a12*(u(N)*v(N-1)-u(N-1)*v(N)-u(N)*v(N)-u(N-1)*v(N-1))/(dx^2);

dv(N) = 2*a22*(v(N-1)-v(N))/(dx^2)+a21*(v(N)*u(N-1)-v(N-1)*u(N)-v(N)*u(N)-v(N-1)*u(N-1))/(dx^2);

for i=2:N-1

du(i) = a11*(u(i+1)-u(i)+u(i-1))/(dx^2)+a12*(u(i)*v(i+1)-u(i-1)*v(i)-u(i)*v(i)-u(i-1)*v(i-1))/(dx^2);

dv(i) = a22*(v(i+1)-v(i)+v(i-1))/(dx^2)+a21*(v(i)*u(i+1)-v(i-1)*u(i)-v(i)*u(i)-v(i-1)*u(i-1))/(dx^2);

end

dy = [du,dv];

Answer 1

[Stephan]

To solve this error make sure that dy is column vector.

dy = [du; dv]

could already solve the problem - but only if they are scalar valued ( I did not check) or are column vectors too.