Rational inversion of the Laplace transform
Journal of Evolution Equations
This paper studies new inversion methods for the Laplace transform of vector-valued functions arising from a combination of A-stable rational approximation schemes to the exponential and the shift operator semigroup. Each inversion method is provided in the form of a (finite) linear combination of the Laplace transform of the function and a finite amount of its derivatives. Seven explicit methods arising from A-stable schemes are provided, such as the Backward Euler, RadauIIA, Crank-Nicolson, and Calahan scheme. The main result shows that, if a function has an analytic extension to a sector containing the nonnegative real line, then the error estimate for each method is uniform in time. © 2012 Springer Basel AG (outside the USA).
Jara, P., Neubrander, F., & Özer, K. (2012). Rational inversion of the Laplace transform. Journal of Evolution Equations, 12 (2), 435-457. https://doi.org/10.1007/s00028-012-0139-1