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Two‐dimensional shifted Legendre polynomial collocation method for electromagnetic waves in dielectric media via almost operational matrices
Author(s) -
Patel Vijay Kumar,
Singh Somveer,
Singh Vineet Kumar
Publication year - 2017
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.4257
Subject(s) - legendre polynomials , mathematics , collocation (remote sensing) , associated legendre polynomials , collocation method , algebraic equation , mathematical analysis , orthogonal collocation , partial differential equation , partial derivative , differential equation , orthogonal polynomials , classical orthogonal polynomials , gegenbauer polynomials , ordinary differential equation , physics , nonlinear system , quantum mechanics , remote sensing , geology
In this paper, a numerical solution of fractional partial differential equations (FPDEs) for electromagnetic waves in dielectric media will be discussed. For the solution of FPDEs, we developed a numerical collocation method using an algorithm based on two‐dimensional shifted Legendre polynomials approximation, which is proposed for electromagnetic waves in dielectric media. By implementing the partial Riemann–Liouville fractional derivative operators, two‐dimensional shifted Legendre polynomials approximation and its operational matrix along with collocation method are used to convert FPDEs first into weakly singular fractional partial integro‐differential equations and then converted weakly singular fractional partial integro‐differential equations into system of algebraic equation. Some results concerning the convergence analysis and error analysis are obtained. Illustrative examples are included to demonstrate the validity and applicability of the technique. Copyright © 2017 John Wiley & Sons, Ltd.