Hermite collocation method for fractional order differential equations

Abstract

This paper focuses on the approximate solutions of the higher order fractional differential equations with multi terms by the help of Hermite Collocation method (HCM). This new method is an adaptation of Taylor's collocation method in terms of truncated Hermite Series. With this method, the differential equation is transformed into an algebraic equation and the unknowns of the equation are the coefficients of the Hermite series solution of the problem. This method appears as a useful tool for solving fractional differential equations with variable coefficients. To show the pertinent feature of the proposed method, we test the accuracy of the method with some illustrative examples and check the error bounds for numerical calculations.

Numerical Study of Time-Fractional Schrödinger Model in One-Dimensional Space Arising in Mathematical Physics

“…Numerous researchers have offered several powerful computational and analytical strategies for determining results for fractional-order differential problems, such as: differential transform scheme [19], new iterative strategy [20], Trial equation strategy [21], Adomian decomposition technique [22], generalized Taylor matrix method [23], Hermite collocation method [24], and many others [25][26][27]. The power series technique [28] is a common and straightforward scheme to find computational results for solving linear differential problems.…”

Analysis of Charge and Current Flow in the LCR Series Circuit via Chebyshev Wavelets

“…have been utilized. Many algorithms utilizing Haar and Hermite wavelets have been created to tackle integral and differential equations and are discussed in Cattani [1,2], Chen and Hsiao [3,4], Lepik [5], Singh [6], Ali et al [7], Pirim and Ayaz [8], and Singh and Kumar [9,10]. The Chebyshev wavelet is a highly effective mathematical tool for solving a range of scientific and engineering problems.…”