Numerical Inverse Laplace Transforms for Electrical Engineering Simulation
Lubomír Brančík · InTech eBooks · 2011
Numerical inverse Laplace transform (NILT) methods are widely used in various scientific areas, especially for a solution of respective differential equations. In field of an electrical engineering many various approaches have been considered so far, but mostly for a single variable (1D NILT), see at least (Brancik, 1999, 2007b; Cohen, 2007; Valsa & Brancik, 1998; Wu at al., 2001) from plenty of papers. Much less attention was paid to multidimensional variable (nD NILT) methods, see e.g. (Hwang at al., 1983; Singhal at al., 1975), useful rather for more complicated electromagnetic systems. The 2D NILT methods, see e.g. (Brancik, 2005, 2007a, 2007b; Hwang & Lu, 1999), can be applied for a transmission line analysis, or nD NILT methods, n ≥ 2, for a nonlinear circuits analysis, if relevant Laplace transforms are developed through a Volterra series expansion, see e.g. (Brancik, 2010a, 2010b, Karmakar, 1980; Schetzen, 2006), to highlight at least a few applications. This paper is focused on the class of NILT methods based on complex Fourier series approximation, their error analysis, their effective algorithms development in a Matlab language, and after all, on their selected applications in field of electrical engineering to show practical usefulness of the algorithms.