Title: New algorithm based on Bernoulli polynomials for the solution of differential equations governing AC circuits

Authors: Sagar Verma; Sandeep Dixit; Shweta Pandey

Addresses: Department of Mathematics, University of Petroleum and Energy Studies (UPES), Dehradun-248007, India ' Department of Mathematics, University of Petroleum and Energy Studies (UPES), Dehradun-248007, India ' Department of Mathematics, VKSC Government Degree College, Dehradun-248007, India

Abstract: In this article, for the purpose of solving differential equations regulating AC circuits (LR, LC and LCR) numerically, a noble approach based on orthonormal Bernoulli polynomials has been developed. The operational matrix of integration is obtained from orthonormal Bernoulli polynomials which convert differential equations into systems of algebraic equations for straightforward computation. It seems that few numbers of orthonormal polynomials provided a better outcome. The exactness and convergence were examined by comparing the calculated numerical solution with the known analytical solution. The absolute error is also calculated and illustrated graphically for reliability and accuracy of the straightforward and easy to use for solution of several differential equations.

Keywords: AC circuits; orthonormal Bernoulli polynomials; operational matrix.

DOI: 10.1504/IJANS.2025.151247

International Journal of Applied Nonlinear Science, 2025 Vol.5 No.2, pp.152 - 162

Received: 23 Aug 2024
Accepted: 06 Nov 2024
Published online: 19 Jan 2026 *

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