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Accuracy Comparison of Some 2D Numerical Inverse Laplace Transform Methods
R-Smith, Nawfal Al-Zubaidi
Numerical Laplace inversions are essential to use when the analytical manipulations of the Laplace transform tables are not possible to apply, and this becomes more and more difficult for applications with higher number of variables. In this paper we describe three methods for 2D numerical inverse Laplace transforms and analyse the methods as for their accuracy and calculation efficiency by implementing them in the Matlab environment. The relative and absolute errors for three different testing functions with previously known originals are presented in a comparative table for the selected points, and the 3D resulting plots for the inversion of a test function are displayed.
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Methods of Numerical Inversion of Laplace Transforms for Electrical Engineering and Their Applications
Al-Zubaidi R-Smith, Nawfal ; Machado,, José Tenreiro (oponent) ; Biolek, Dalibor (oponent) ; Brančík, Lubomír (vedoucí práce)
Numerical inverse Laplace transform (NILT) methods have become a fundamental part of the numerical toolset of practitioners and researchers in a large number of science and engineering fields, especially in the electrical engineering applied domain. Mainly, NILT techniques assist in getting the time-domain simulations in related applications, e.g. solving ordinary differential equations as those appearing when solving lumped-parameter circuits, solving partial differential equations as in linear distributed-parameter systems or those emerging while investigating signal integrity issues. Generally, most available 1D NILT methods are very specific, i.e. they perform well on a few types of functions and hence on a limited number of applications; thus the aim of this research is to provide a broad treatment of such numerical methods, the development of universal NILT method and its expansion to multidimensional NILT which can cover a wide field of applications and could provide a practical mechanism for a better diagnosis and analysis of time domain simulations. The reach of the ideas is presented by discussing a wide range of case studies and applications; for example, the NILT methods are applied in solving transmission lines, including multiconductor ones, and even for the solution of weakly nonlinear circuits while utilizing multivariable NILTs. With the assistance of the NILT method, an advantage of including frequency dependent parameters and using fractional order elements in their respective models can be done in a very accurate and simple manner.
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Methods of Numerical Inversion of Laplace Transforms for Electrical Engineering and Their Applications
Al-Zubaidi R-Smith, Nawfal ; Machado,, José Tenreiro (oponent) ; Biolek, Dalibor (oponent) ; Brančík, Lubomír (vedoucí práce)
Numerical inverse Laplace transform (NILT) methods have become a fundamental part of the numerical toolset of practitioners and researchers in a large number of science and engineering fields, especially in the electrical engineering applied domain. Mainly, NILT techniques assist in getting the time-domain simulations in related applications, e.g. solving ordinary differential equations as those appearing when solving lumped-parameter circuits, solving partial differential equations as in linear distributed-parameter systems or those emerging while investigating signal integrity issues. Generally, most available 1D NILT methods are very specific, i.e. they perform well on a few types of functions and hence on a limited number of applications; thus the aim of this research is to provide a broad treatment of such numerical methods, the development of universal NILT method and its expansion to multidimensional NILT which can cover a wide field of applications and could provide a practical mechanism for a better diagnosis and analysis of time domain simulations. The reach of the ideas is presented by discussing a wide range of case studies and applications; for example, the NILT methods are applied in solving transmission lines, including multiconductor ones, and even for the solution of weakly nonlinear circuits while utilizing multivariable NILTs. With the assistance of the NILT method, an advantage of including frequency dependent parameters and using fractional order elements in their respective models can be done in a very accurate and simple manner.
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Accuracy Comparison of Some 2D Numerical Inverse Laplace Transform Methods
R-Smith, Nawfal Al-Zubaidi
Numerical Laplace inversions are essential to use when the analytical manipulations of the Laplace transform tables are not possible to apply, and this becomes more and more difficult for applications with higher number of variables. In this paper we describe three methods for 2D numerical inverse Laplace transforms and analyse the methods as for their accuracy and calculation efficiency by implementing them in the Matlab environment. The relative and absolute errors for three different testing functions with previously known originals are presented in a comparative table for the selected points, and the 3D resulting plots for the inversion of a test function are displayed.
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