Solving Some Differential Equations Arising in Electric Engineering Using Hermite Polynomials

Abstract

In this paper, a collocation method based on Hermite polynomials is presented for the numerical solution of the electric circuit equations arising in many branches of sciences and engineering. By using collocation points and Hermite polynomials, electric circuit equations are transformed into a system of linear algebraic equations with unknown Hermite coefficients. These unknown Hermite coefficients have been computed by solving such algebraic equations. To illustrate the accuracy of the proposed method some numerical examples are presented.

Numerical Solution of Cahn-Allen Equations by Wavelet Based Lifting Schemes

“…But now that powerful software and contemporary computers have been developed, it is possible to use analytical or numerical methods to solve these issues [1]. Recently, methods have been utilized to solve partial differential equations, both linear and nonlinear, numerically and analytically, for instance, Hermite polynomials [2], a comprehensive approximation system based on biorthogonal wavelets [3], the Adomian Decomposition Method and Haar Wavelet Method [4] etc.…”

An Effective Computational Approach Based on Hermite Wavelet Galerkin for Solving Parabolic Volterra Partial Integro Differential Equations and Its Convergence Analysis

“…There are a few orthogonal wavelet methods that can provide a tangible level of accuracy which are considered by researchers. The Hermite polynomial-based wavelet techniques can offer a better solution because they reduce the computational cost at a tangible level and provide a better rate of accuracy [22].…”

“…Using orthogonal basis functions tends to reduce the effects of rounding errors that occur when computing the approximation. Hermite wavelets have been widely applied in numerical solution of differential equations [22], boundary value problems [2], singular initial value problems [21], integral equations [12], integro-differential equations [9].…”