Using differential equations in electrical circuits' simulation

Computers & Electrical Engineering, 28(6), 513-525, 2000

An effective but not widely used method, differential Taylor transform, is introduced for the analysis of the nonlinear electrical circuits. To apply the method the differential transform of the mathematical model of the system is obtained first, and then the response function is evaluated by using the inverse transform of the differential spectra. The inverse transform can be written in the form of Taylor series. The method is described with two examples for nonlinear electrical circuits.

Mathematical and Computational Applications

The RLC circuit is a basic building block of the more complicated electrical circuits and networks. The present study introduces a novel and simple numerical method for the solution this problem in terms of Taylor polynomials in the matrix form. Particular and general solutions of the related differential equation can be determined by this method. The method is illustrated by a numerical application and a quite good agreement is observed between the results of the present method and those of the exact method.

Asian journal of applied science and technology, 2022

This paper presents the derivation and implementation of a computational approach for the solution of some electric circuit problems. The one-step computational hybrid block method was developed using Legendre polynomial of degree six as our basis function via interpolation and collocation techniques. The computational method developed was applied on some practical problems in electricity to generate graphical results and also interpret the natures of these results. The paper went further to analyze the basic properties of the computational method derived. From the graphical results obtained, the computed solutions converge toward the exact solutions.

Applied Mathematics and Computation, 2004

In this paper, the method is developed to differential-algebraic equations systems. More effective method is presented and illustrated by numerical example. The solution for a differential-algebraic equation can be expanded up to arbitrary order using MAPLE computer algebra systems. First we calculate power series of the given equations system then transform it into Pad e series form, which give an arbitrary order for solving differential-algebraic equation numerically.

UNEC journal of engineering and applied sciences, 2024

The generalized classical method (GCM) was developed on the basis of the differential Taylor transform method, which was first used by the Ukrainian scientist G.E. Pukhov. In this study, some applications of the GCM to the analysis of transient events in simple electrical circuits are examined. It is shown that, if the solution can be decomposed into a steady-state part and a transient part, the use of the GCM becomes more effective, and the transient regime of the circuit solution can be analyzed without a full solving process of differential equations. The efficiency of the proposed approximation method is illustrated by comparing it with prior arts on similar problems. The results reveal that the proposed method is simple and can be applied successfully for the analysis of both linear and nonlinear problems in mathematical physics by similar solving procedures.

In this paper, Differential Transformation Method DTM is introduced to study the singular system of a linear electrical circuit for time invariant and time varying cases. The discrete solutions obtained using DTM are compared with the exact solutions of the electrical circuit problem and are found to be very accurate and compatible. Graphs for inductor currents and capacitor voltages are presented to show the efficiency of DTM.

TELKOMNIKA Telecommunication Computing Electronics and Control, 2019

We investigate the validity of the formal expansion method for solving a second order ordinary differential equation raised from an electrical circuit problem. The formal expansion method approximates the exact solution using a series of solutions. An approximate formal expansion solution is a truncated version of this series. In this paper, we confirm using simulations that the approximate formal expansion solution is valid for a specific interval of domain of the free variable. The accuracy of the formal expansion approximation is guaranteed on the timescale 1.

Progress in Industrial Mathematics at ECMI 2006, 2008

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Mathematical Programming, 2010

Modern modeling approaches for circuit analysis lead to differentialalgebraic equations (DAEs). The index of a DAE is a measure of the degree of numerical difficulty. In general, the higher the index is, the more difficult it is to solve the DAE. The index of the DAE arising from the modified nodal analysis (MNA) is determined uniquely by the structure of the circuit. Instead, we consider a broader class of analysis method called the hybrid analysis. For linear time-invariant electric circuits, we devise a combinatorial algorithm for finding an optimal hybrid analysis in which the index of the DAE to be solved attains the minimum. The optimal hybrid analysis often results in a DAE with lower index than MNA.

1978

Abstmct-In tlds paper we describe a method of generating families of iterative algorithms which are suitable for solving nonlinear systems of equations. 'l&se families of algorithms, one of which includes the Newton-Raphson algorithm as a special case, are novel in that they could use the type and behavior of each of the individual equations to advantage; in effect, the algorithms are able to tailor themselves to the behavior of each function. In addition, by suitably choosing from among the members of one of these families of iterative schemes, a variable-order algorithm emergea. For one such family, this variable-order algorithm is equivalent to the heuristic modifications of the Newton-Raphson algorithm that have been proposed wbicb do not update the Jacobian at every iteration. The question of bow often tbe Jacobian should be updated can thus be discus.4 from a theoretical as well as an experimental viewpoint. Preliminary results indicate tbat the variable-order algorithms can provide significant computational savings in a transient simulation when compared with the conventional Newtou-Rap&n algorithm.