d63127f2385212b8f5280af2b72980df electronics-13-02480-v2.pdf 1bfa8a528898b886f2b438e79ca4e77f074ec735 electronics-13-02480-v2.pdf 9cf8d754577ea98f6fbec290017b31d8ad3a8dfd0deacada4471c3521f87dc42 electronics-13-02480-v2.pdf Title: The Method of Elementary Solvers in SPICE Subject: Circuit simulators are fundamentally used for solving electric circuit problems with different degrees of complexity in which node voltages and branch currents are the unknowns. This is fully understandable since they were originally created for this specific task. However, behind the curtains, powerful simulation engines based on a variety of numerical techniques operate so as to always comply with Kirchhoff’s current and voltage laws. In this paper, it is shown how a simple circuital configuration, referred to as the elementary solver, consistent in two behavioral current sources in series, can be used to solve mathematical problems that go beyond electronics. Of course, the intention is not to substitute mathematical packages with well-proven calculus capacity but to increase the scope of circuit simulators for their application in other areas of research or simply for educational purposes. It is worth mentioning that no special programming skills are required (except a basic knowledge of the available tools and language) and, furthermore, that the user can operate exclusively in a graphical environment. It is shown, throughout a series of selected examples, how the method of elementary solvers (MES) works, providing a new and practical dimension to the applicability of circuit simulators. Keywords: circuit simulator; LTSpice; SPICE; modeling; simulation; differential equations;problem solving Author: Enrique Miranda Creator: LaTeX with hyperref Producer: pdfTeX-1.40.25 CreationDate: Wed Jul 10 11:16:43 2024 CEST ModDate: Wed Jul 10 11:21:53 2024 CEST Custom Metadata: no Metadata Stream: no Tagged: no UserProperties: no Suspects: no Form: none JavaScript: no Pages: 24 Encrypted: no Page size: 595.276 x 841.89 pts (A4) Page rot: 0 File size: 6505439 bytes Optimized: no PDF version: 1.7 name type encoding emb sub uni object ID ------------------------------------ ----------------- ---------------- --- --- --- --------- CQZVIY+VnURWPalladioL Type 1 Custom yes yes yes 10 0 UDOHRI+URWPalladioL-Bold Type 1 Custom yes yes yes 16 0 PTTNDL+URWPalladioL-Roma Type 1 Custom yes yes yes 22 0 VWQFEH+URWPalladioL-Ital Type 1 Custom yes yes yes 27 0 GKSXYT+TimesNewRomanPS-BoldItalicMT Type 1C WinAnsi yes yes no 43 0 BNUKMV+PazoMath Type 1 Builtin yes yes yes 60 0 LWGQQX+CMSY10 Type 1 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1314 0 Jhove (Rel. 1.28.0, 2023-05-18) Date: 2024-11-14 02:53:12 CET RepresentationInformation: electronics-13-02480-v2.pdf ReportingModule: PDF-hul, Rel. 1.12.4 (2023-03-16) LastModified: 2024-09-20 14:01:23 CEST Size: 6505439 Format: PDF Version: 1.7 Status: Well-Formed and valid SignatureMatches: PDF-hul MIMEtype: application/pdf PDFMetadata: Objects: 1482 FreeObjects: 1 IncrementalUpdates: 0 DocumentCatalog: PageLayout: SinglePage PageMode: UseNone Outlines: Item: Title: Introduction Destination: section.1 Item: Title: Selected Examples Destination: section.2 Children: Item: Title: Solution of a Nonlinear Equation: Lambert W Function Destination: subsection.2.1 Item: Title: Analysis of a Function: Polynomial Case Destination: subsection.2.2 Item: Title: Indirect Integration: Gamma Function Destination: subsection.2.3 Item: Title: Recursion: Explicit Newton Raphson Method Destination: subsection.2.4 Item: Title: System of Linear Equations: Matrix Inversion Destination: subsection.2.5 Item: Title: System of Nonlinear Equations: Optimum Solution Destination: subsection.2.6 Item: Title: First-Order Autonomous Differential Equation: Newton’s Law of Heat Transfer Destination: subsection.2.7 Item: Title: First-Order Non-Autonomous Differential Equation: Redefinition of the Time Coordinate Destination: subsection.2.8 Item: Title: Delayed Differential Equation: Logistic Model Destination: subsection.2.9 Item: Title: First-Order Integro-Differential Equation: When Integrals and Derivatives Meet Destination: subsection.2.10 Item: Title: Second-Order Differential Equation: Harmonic Oscillator Destination: subsection.2.11 Item: Title: Differential Equation with Control Parameter: Frequency-Dependent Memristor Model Destination: subsection.2.12 Item: Title: System of Nonlinear Differential Equations: Lotka Volterra Model Destination: subsection.2.13 Item: Title: Recurrence Relation: Logistic Map Destination: subsection.2.14 Item: Title: System of Nonlinear Differential Equations: SIR Model with Vital Dynamics Destination: subsection.2.15 Item: Title: System of Nonlinear Differential Equations: Lorenz Model Destination: subsection.2.16 Item: Title: Discrete Fractal Curve: 2D Random Walk Destination: subsection.2.17 Item: Title: Parabolic Partial Differential Equation: 1D Heat Equation Destination: subsection.2.18 Item: Title: Hyperbolic Partial Differential Equation: 1D Wave Equation Destination: subsection.2.19 Item: Title: Stochastic Differential Equation: Ornstein Uhlenbeck Process Destination: subsection.2.20 Item: Title: Control System: When Physics Meets Mathematics Meets Electronics Destination: subsection.2.21 Item: Title: Conclusions Destination: section.3 Item: Title: References Destination: appendix.A. Info: Title: The Method of Elementary Solvers in SPICE Author: Enrique Miranda Subject: Circuit simulators are fundamentally used for solving electric circuit problems with different degrees of complexity in which node voltages and branch currents are the unknowns. This is fully understandable since they were originally created for this specific task. However, behind the curtains, powerful simulation engines based on a variety of numerical techniques operate so as to always comply with Kirchhoff’s current and voltage laws. In this paper, it is shown how a simple circuital configuration, referred to as the elementary solver, consistent in two behavioral current sources in series, can be used to solve mathematical problems that go beyond electronics. Of course, the intention is not to substitute mathematical packages with well-proven calculus capacity but to increase the scope of circuit simulators for their application in other areas of research or simply for educational purposes. It is worth mentioning that no special programming skills are required (except a basic knowledge of the available tools and language) and, furthermore, that the user can operate exclusively in a graphical environment. It is shown, throughout a series of selected examples, how the method of elementary solvers (MES) works, providing a new and practical dimension to the applicability of circuit simulators. 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