Open AccessA New Algorithm Based on Bernstein Polynomials Multiwavelets for the Solution of Differential Equations Governing AC Circuits
Author(s) -
Shweta Pandey,
S. P. Dixit,
Sag Ram Verma
Publication year - 2021
Publication title -
trends in sciences
Language(s) - English
Resource type - Journals
ISSN - 2774-0226
DOI - 10.48048/tis.2021.33
Subject(s) - mathematics , polynomial , differential equation , convergence (economics) , matrix (chemical analysis) , algebraic equation , bernstein polynomial , wavelet , computation , system of linear equations , mathematical analysis , algorithm , computer science , nonlinear system , materials science , physics , quantum mechanics , artificial intelligence , economics , composite material , economic growth
We extend the application of multiwavelet-based Bernstein polynomials for the numerical solution of differential equations governing AC circuits (LCR and LC). The operational matrix of integration is obtained from the orthonormal Bernstein polynomial wavelet bases, which diminishes differential equations into the system of linear algebraic equations for easy computation. It appeared that fewer wavelet bases gave better results. The convergence and exactness were examined by comparing the calculated numerical solution and the known analytical solution. The error function was calculated and illustrated graphically for the reliability and accuracy of the proposed method. The proposed method examined several physical issues that lead to differential equations.HIGHLIGHTSDifferential equations governing AC circuits are converted into the system of linear algebraic equations using Bernstein polynomial multiwavelets operational matrix of integration for easy computationThe convergence and exactness were examined by comparing the calculated numerical solution and the known analytical solutionThe error function is calculated and shown graphicallyGRAPHICAL ABSTRACT