How to fix this error Index exceeds the number of array elements (1) for a linear advection problem ?

Question

Zahraa 2020-9-28

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https://ww2.mathworks.cn/matlabcentral/answers/601405-how-to-fix-this-error-index-exceeds-the-number-of-array-elements-1-for-a-linear-advection-problem

回答： Walter Roberson 2020-9-29

the problem statement is a linear advection equation with these following conditions

and use grid spacing of dx=1 and apply time setp dt based on CFL numbers 0.5,0.8,1.0. Compute the solution for 100 time steps. To solve this problem I have to use explicit upwind differencing (FTBS).

here is my attempted code, I'm not sure how to fix this code

%define variable 
xmin = 0;        %min value of x
xmax = 250;      %max value of x
dx=1; 
c=250;           %velcoity
CFL=0.5;
dt=(CFL*dx)/c;  
tmax = 100;     % max value of t
t=0;            %time 
N=100;          %number of nodes-1
% discretise the domain 
x=xmin:dx:xmax;
%set initial condition 
for i=1:xmax 
    if (0<=x(i))&&(x(i)<=50)
       u0=0;
    elseif (50<=x(i))&&(x(i)<=110)
        u0=100*sin(pi*(x-50)/60);
    else (110<=x(i))&&(x(i)<=250);
        u0=0;
    end 
   
end 
% loop through time 
nsteps = tmax/dt;
for n=1:nsteps
     u=u0;
     unp1=u0;
    %Boundary conditions
     u(:)=0;
     
    %upwind scheme 
    for i = 2:N+2
        unp1(i)=u(i)-CFL*(u(i)-u(i-1));
    end 
    %update t and u 
    t = t+dt;
    u = unp1; 
    
    %Plot solution 
    plot(x,u,'bo-','markerfacecolor','b');
    pause(0.01);
    
end 

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KSSV 2020-9-29

Your u is a scalr and you are trying to access it like a vector.

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Answer 1

Walter Roberson 2020-9-29

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https://ww2.mathworks.cn/matlabcentral/answers/601405-how-to-fix-this-error-index-exceeds-the-number-of-array-elements-1-for-a-linear-advection-problem#answer_502480

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for i=1:xmax 
    if (0<=x(i))&&(x(i)<=50)
       u0(i)=0;
    elseif (50<=x(i))&&(x(i)<=110)
        u0(i)=100*sin(pi*(x-50)/60);
    else (110<=x(i))&&(x(i)<=250);
        u0(i)=0;
    else
        u0(i)=nan;
    end 
end 