کد متلب روش های عددی، مثال های کتاب سادیکو، فصل 3، مثال 3-2

% Numerical Techiniques in Electromagnetics

% MATLAB code for example 3.2 on  one-dimensional wave equation solved

% using an explicit finite difference scheme

clear all; format compact; tic

%Explicit Method

    delx = 0.1;         % resolution size

    r = 1;              % 'aspect ratio' 

    u = 1;              % Constant of given wave equation

    delt = r^2*delx/u;  % time step size

    Tsteps = round(1/delt); % Number of time steps

    

    % X1 is the potential grid of the simulation, due to symetry only half

    % of the field is calculated.

    X1 = zeros(Tsteps,1/(2*delx)+2);    % Initilize X1

    %Initial conditions and reflection line defined

    x = 0:delx:.5+delx; 

    X1(1,:) = sin(pi*x);

    X1(2,2:end-1) = .5*(X1(1,1:end-2)+X1(1,3:end));

    X1(2,end) = X1(2,end-2); %reflection line

    for row = 3:size(X1,1)

        for col = 2:size(X1,2)-1

            X1(row,col) = X1(row-1,col-1)+X1(row-1,col+1)-X1(row-2,col); % eqn. (3.26)

        end

        X1(row,end) = X1(row,end-2);    %reflected line

    end

    

    %Use symetry condition to create entire field

    X2 = [X1,fliplr(X1(:,1:end-3))];

    figure(1),imagesc(0:delx:1,(0:delt:Tsteps*delt),X2),colorbar

        ylabel('\leftarrow time (sec)')

        xlabel('x')

        title('Hyperbolic PDE')

        

    if (delx==.1)

        dispmat = [X1(1:8,1:7)];        

        disp(sprintf('\nCompare to Table 3.5, Solution of the Wave Equation in Example 3.2'))   

        disp(num2str(dispmat))

    end

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