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% Applies BTCS algorithm for given parameters and returns:
%   1. the solution in matrix form (QnMax) with added boundary conditions
%   2. grid points on x and y axis (xg, yg)
%   3. total times needed to form Laplace matrix and to solve linear system
%   (mat_time, sol_time)
function [QnMat, xg, yg, mat_time, sol_time] = BTCS(alpha, dt, t0, tmax, Nx, Ny)
    xg = -1:2/(Nx-1):1;
    yg = -0.5:1/(Ny-1):0.5;

    BCf = @(x,y) exp(1-x^2-y^2)*sin(x^2+y^2);

    nL = (Nx-2)*(Ny-2);

    % Starting values are all zeros, outside boundaries
    Qn = zeros(nL,1);

    % matrix formation time and linear system solution time
    mat_time = 0;
    sol_time = 0;
   
    for t=t0+dt:dt:tmax
       % form the Laplace matrix and its RHS side from boundary conditions
       tic;
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        1.48mstwenty4_siteHomeworkLibraryController.php#97
        Backtrace
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        • 22. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
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        • 23. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
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        • 26. app/Http/Controllers/HomeworkLibraryController.php:105
        • 27. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 28. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
        • 29. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
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      • select * from `subjects` where `subjects`.`id` in (395)
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        Backtrace
        • 19. app/Repositories/HomeworkLibraryRepository.php:30
        • 20. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
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      • select * from `solutionslibrary_files` where `solutionslibrary_files`.`solutionlib_id` = 61698 and `solutionslibrary_files`.`solutionlib_id` is not null and `publish` = 'question' order by `order` asc, `id` asc
        1.1mstwenty4_siteHomeworkLibrary.php#260
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        Backtrace
        • 15. app/Models/HomeworkLibrary/HomeworkLibrary.php:260
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        • 19. vendor/league/fractal/src/TransformerAbstract.php:128
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