File: laxexplicit.m Line: 41 Column: 31 Invalid expression. When calling a function or indexing a variable, use parentheses. Otherwise, check for mismatched delimiters.

% Chlorine Decay Flow for the Lax method to solve the advection equation

clear;

% Parameters to definr the advection equation and the range in space and time

D = 1*10^-4; % Heat Conductivity parameter in m2/s

K = 1*10^-4; % Heat Conductivity parameter in s^-1Lmax=100; % Maximum Length in m

Tmax = 43200.; % Maximum time

C = 1.0; % Advection velocity

% Parameters needed to implement the Lax method

Nt = 6; % Number of time steps

Dt = 1; % Time step in seconds

Nx = 51; % Number of space steps

Dx = 0.5; % space step in m

b = -K; % beta parameter in the finite-difference implementation

% Remember that the Lax method is stable for b=< 1/2 but it gets diffused unless abs(b) = 1/2

% Initial condition: the initial value of the u function (amplitude of the wave initially)

Nfront = round(Nx/2); % The wave-front: intermediate point from which u=0

for i =1:(Nx+1)

if i <Nfront

u(i,1)=1.;

else

u(i,1)=0.;

end

x(i)= (i-1)*Dx; % we also define vector x, due to space discretization

end

% Boundary conditions: value of the u function at the boundaries at any time

for k=1:Nt+1

u(1,k) =1.;

u(Nx+1,k)= 0.;

t(k) = (k-1)*Dt; % we also define vector t, due to the time discretization

end

% Implementation of the Lax mathod

for k=1:Nt %Time loop

for i =2:Nx % Space loop

u(i,k+1) = 1/2*(u(i+1),k + u(i-1),k) - D*Dt/2*Dx*(u(i+1),k-u(i-1),k);

end

end

% Graphical representations of the evolution of the pipe

plot(x,u(:,1), '-b',x,u(:,round(Nt/10)),'--g',x,u(:,round(Nt/3)),':b',x,u(:,Nt),'-.r')

Title ('Pipe flow test within Lax method')

xlabel('X')

ylabel('Amplitude(X)')

I need to plot my profile C vs x at t =[2,4,6,8,10,12]

I think i messed up the labelling part

Answer 1

[Voss]

There were some syntax errors in the calculation of u(i,k+1). I made a guess at fixing them. (And another syntax error in "Title" - should be "title".) See if it looks right now:

% Chlorine Decay Flow for the Lax method to solve the advection equation
clear;
% Parameters to definr the advection equation and the range in space and time
D = 1*10^-4;               % Heat Conductivity parameter in m2/s
K = 1*10^-4;               % Heat Conductivity parameter in s^-1Lmax=100;                 % Maximum Length in m 
Tmax = 43200.;            % Maximum time
C = 1.0;                  % Advection velocity
% Parameters needed to implement the Lax method
Nt = 6;                    % Number of time steps
Dt = 1;                    % Time step in seconds
Nx = 51;                   % Number of space steps
Dx = 0.5;                  % space step in m
b = -K;                     % beta parameter in the finite-difference implementation
% Remember that the Lax method is stable for b=< 1/2 but it gets diffused unless abs(b) = 1/2
% Initial condition: the initial value of the u function (amplitude of the wave initially)
Nfront = round(Nx/2); % The wave-front: intermediate point from which u=0
for i =1:(Nx+1)
    if i <Nfront
        u(i,1)=1.;
    else
        u(i,1)=0.;
    end
    x(i)= (i-1)*Dx; % we also define vector x, due to space discretization
end
% Boundary conditions: value of the u function at the boundaries at any time
for k=1:Nt+1
    u(1,k) =1.;
    u(Nx+1,k)= 0.;
    t(k) = (k-1)*Dt; % we also define vector t, due to the time discretization
end
% Implementation of the Lax mathod
for k=1:Nt            %Time loop
    for i =2:Nx       % Space loop
        
%         u(i,k+1) = 1/2*(u(i+1),k + u(i-1),k) - D*Dt/2*Dx*(u(i+1),k-u(i-1),k);
        u(i,k+1) = 1/2*(u(i+1,k) + u(i-1,k)) - D*Dt/2*Dx*(u(i+1,k) - u(i-1,k));
        
    end
end
% Graphical representations of the evolution of the pipe
plot(x,u(:,1), '-b',x,u(:,round(Nt/10)),'--g',x,u(:,round(Nt/3)),':b',x,u(:,Nt),'-.r')

% Title ('Pipe flow test within Lax method')
title('Pipe flow test within Lax method')

xlabel('X')
ylabel('Amplitude(X)')