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Chebpack

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Chebpack

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15 Jul 2011 (Updated )

The MATLAB package Chebpack solves specific problems for differential or integral equations.

[x,solnum]=fred_eq(n,dom,kind)
function [x,solnum]=fred_eq(n,dom,kind)
% Solves Fredholm integral equations
% y(x)=int_a^b(K(x,t)y(t)dt+f(x), x in [a,b]
% 
tic;
K=fred(n,dom,kind);
F=x2t(myfun(x),kind);
sol=(speye(n)-K)\F;% solution in the spectral space
solnum=t2x(sol,kind);% solution in the physical space
toc;myOUT
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function [Fspec,Fphys]=fred(n,dom,kind)
% Fredholm operator with kernel K(x,t)
[x,w]=pd(n,dom,kind);T=cpv(n,x,dom);
[Y,X]=meshgrid(x,x);KW=mykernel(X,Y);
Fphys=KW*diag(w);Fspec=T\Fphys*T;
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function col=mykernel(x,t)
    % describes K(x,t), x,t matrices
    % must be written by the user
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function f=myfun(x)
    % describes f(x) 
    % must be written by the user
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function myOUT
    % describes the output of the code
    % must be written by the user
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
end

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