% Numerical Inversion of Laplace Transforms: 
% The Zakian Method

% Author's Data: Housam BINOUS
% Department of Chemical Engineering
% National Institute of Applied Sciences and Technology
% Tunis, TUNISIA
% Email: binoushousam@yahoo.com 

% We perform numerical inversion of F(s)=1/(s^2*(s+1)^2)
% Result is compared to the analytical solution
% f(t)=t*exp(-t)+t-2+2*exp(-t)


t=0.01:0.01:10;

a=[(1.283767675e+1)+i*1.666063445,(1.222613209e+1)+i*5.012718792,...
    (1.09343031e+1)+i*8.40967312,8.77643472+i*1.19218539e+1,...
    5.22545336+i*1.57295290e+1];

K=[(-3.69020821e+4)+i*1.96990426e+5,(6.12770252e+4)-i*9.54086255e+4,...
      -(2.89165629e+4)+i*1.81691853e+4,(4.65536114e+3)-i*1.90152864,...
      -(1.18741401e+2)-i*1.41303691e+2]; 

f=zeros(1,1000);

for p=1:5
    f=f+real(K(p).*1./(a(p)./t).^2.*1./(a(p)./t+1).^2);
end;

f=2./t.*f;

plot(t,f,'r*')

hold on

plot(t,exp(-t).*t+t-2+2*exp(-t))