# ERROR came as "Index exceeds matrix dimensions".

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MINATI PATRA on 18 Aug 2019
Commented: MINATI PATRA on 24 Aug 2019
%% When I incorporate 3 eqns, ERROR came as "Index exceeds matrix dimensions".
%%Here I have initial condition f=[0 0 0 ], BC: gl=[coswt t t], gr =[0 0 0 ].
What next?
Here is my trial:
H=10;R=5;Pr=1;G1=5;G2=5;Kc=1;Sc=0.22;wt=pi/2;Q=H-(R/Pr);
xl=0; xr=5; % x domain [xl,xr]
J = 10; % J: number of division for x
dx = (xr-xl)/ J; % dx: mesh size
tf = 01; % final simulation time
Nt = 100; % Nt: number of time steps
dt = tf/Nt;
mu = dt/(dx)^2;
% Evaluate the initial conditions
x = xl : dx : xr; % generate the grid point
% f(1:J+1) since array index starts from 1
f1 = 0;f2 = 0;f3 = 0; %%%I.C
% store the solution at all grid points for all time steps
u = zeros(J+1,Nt);
v = zeros(J+1,Nt);
w = zeros(J+1,Nt);
U=[u; v; w];
% Find the approximate solution at each time step
for n = 1:Nt
t = n*dt; % current time
% boundary condition at left side
gl = [cos(wt); t; t];
% boundary condition at right side
gr = [0; 0; 0];
if n==1 % first time step
for j=2:J % interior nodes
u(j,n) = (1+dt*Q)*f1(j) + dt*(G1*f2(j)+G2*f3(j))+mu*(f1(j+1)-2*f1(j)+f1(j-1));
v(j,n) = (1+dt*Q)*f2(j) + (mu/Pr)*(f2(j+1)-2*f2(j)+f2(j-1));
w(j,n) = (1-dt*Kc)*f3(j) + (mu/Sc)*(f3(j+1)-2*f3(j)+f3(j-1));
U=[u(j,n) v(j,n) w(j,n)];
end
U(1,n) = gl; % the left-end point
U(J+1,n) = gr; % the right-end point
else
for j=2:J % interior nodes
u(j,n)= (1+dt*Q)*u(j,n-1)+ dt*(G1*v(j,n-1)+G2*w(j,n-1))+ mu*(u(j+1,n-1)-2*u(j,n-1)+u(j-1,n-1));
v(j,n)= (1+dt*Q)*v(j,n-1)+ (mu/Pr)*(v(j+1,n-1)-2*v(j,n-1)+v(j-1,n-1));
w(j,n)= (1+dt*Q)*w(j,n-1)+ (mu/Sc)*(w(j+1,n-1)-2*w(j,n-1)+w(j-1,n-1));
U=[u(j,n) v(j,n) w(j,n)];
end
U(1,n) = gl; % the left-end point
U(J+1,n) = gr; % the right-end point
end
end
% Plot the results
tt = dt : dt : Nt*dt;
figure(1)
plot(x,u)
hold on
madhan ravi on 18 Aug 2019

Adam Danz on 18 Aug 2019
Edited: Adam Danz on 18 Aug 2019
f1 = 0; % 12th line of your code; so, f1 only has 1 element
for j=2:J % interior nodes
u(j,n) = (1+dt*Q)*f1(j) + dt*(G1*f2(j)+G2*f3(j))+mu*(f1(j+1)-2*f1(j)+f1(j-1));
% ^^^^
When j = 2, you're trying to reference the 2nd element of f1 but f1 only has 1 element.
Walter Roberson on 19 Aug 2019
% boundary condition at left side
gl = [cos(wt); t; t];
What is that intended to designate?
Is the intention that the first row should be assigned the boundary condition cos(wt) (the first entry) and that the last row should be assigned the boundary condition t (the last entry), and that all other rows should be assigned the boundary condition t (the middle entry) ?

MINATI PATRA on 20 Aug 2019
Dear Walter
Please see Equation (12), (Attached pdf)
2nd line is for gl
3rd line is for gr
MINATI PATRA on 24 Aug 2019
Its not working

MINATI PATRA on 21 Aug 2019
u, θand ϕ are coded in u, v and w respectively.