A regularization method for approximating the inverse Laplace transform

A new method for approximating the inerse Laplace transform is presented. We first change our Laplace transform equation into a convolution type integral equation, where Tikhonov regularization techniques and the Fourier transformation are easily applied. We finally obtain a regularized approximation to the inverse Laplace transform as finite sum $$f\left( t \right) \cong \sum\limits_{b \approx 0}^N {b_k \left( \alpha \right)\frac{{d^h G\left( x \right)}} {{dx^h }}}$$ , where b_k(a) are precalculated and tabulated regularization coefficients, G(x)=e^x(e^x) and g(x) is the given Laplace transform of f(t). Error bounds together with an algorithm to calculate the coefficients b_k (a) and some examples are also discussed. Perturbed data problems are not included.