Two approaches to derive approximate formulae of NILT method with generalization

The paper deals with relationship between two approaches to derive approximate formulae of one specific numerical inverse Laplace transform (NILT) method, which is based on the approximation of the exp(st) function in the definition Bromwich integral, and the method based on the direct numerical integration of this ILT integral. It is shown that respective approximate formulae can also be derived by integrating the Bromwich integral numerically provided the integration path and the step are properly chosen as time-dependent. The generalization of the NILT formulae is also suggested leading to possibility to predict a limiting absolute error. The experimental error analysis is performed in the Matlab program for properly chosen Laplace transforms, and modified usage of Euler transformation to accelerate convergence of infinite series is tested successfully.