A hybrid wavelet-meshless method for variable-order fractional regularized long-wave equation. (September 2022)

• Record Type: Journal Article
• Authors: Hosseininia, M.; Heydari, M.H.; Avazzadeh, Z.
• Is Part Of: Engineering analysis with boundary elements. Volume 142(2022)
• Page Start: 61
• Page End: 70
• Publication Date: 2022-09
• Subjects: Variable-order fractional derivative -- Legendre cardinal wavelets -- Radial basis functions -- Fractional regularized long-wave equation; Boundary element methods -- Periodicals; Engineering mathematics -- Periodicals; Équations intégrales de frontière, Méthodes des -- Périodiques; Mathématiques de l'ingénieur -- Périodiques; Boundary element methods; Engineering mathematics; Periodicals; 620.00151
• DOI: 10.1016/j.enganabound.2022.05.021
• Languages: English
• ISSNs: 0955-7997

Abstract

Abstract: This study employs a kind of non-singular variable-order fractional derivative to define a variable-order fractional version of the 2D regularized long-wave equation. The Legendre cardinal wavelets as a new family of the cardinal wavelets are introduced. A hybrid method based on the Legendre cardinal wavelets and radial basis functions is established to find the solution of this problem. This approach turns solving this equation into finding the solution of a nonlinear system of algebraic equations without utilizing discretization. The accuracy of the proposed technique is checked by solving four examples.