A regularization method for the numerical inversion of the Laplace transform
SIAM Journal on Numerical Analysis
An iterative method for the numerical inversion of Laplace transforms
Mathematics of Computation
Numerical analysis: an introduction
Numerical analysis: an introduction
Journal of Computational and Applied Mathematics
Journal of Computational and Applied Mathematics
Hi-index | 7.29 |
Let T,U be two linear operators mapped onto the function f such that U(T(f))=f, but T(U(f))f. In this paper, we first obtain the expansion of functions T(U(f)) and U(T(f)) in a general case. Then, we introduce four special examples of the derived expansions. First example is a combination of the Fourier trigonometric expansion with the Taylor expansion and the second example is a mixed combination of orthogonal polynomial expansions with respect to the defined linear operators T and U. In the third example, we apply the basic expansion U(T(f))=f(x) to explicitly compute some inverse integral transforms, particularly the inverse Laplace transform. And in the last example, a mixed combination of Taylor expansions is presented. A separate section is also allocated to discuss the convergence of the basic expansions T(U(f)) and U(T(f)).