An efficient approach based on Legendre-Gauss–Lobatto quadrature and discrete shifted Hahn polynomials for solving Caputo–Fabrizio fractional Volterra partial integro-differential equations

2021 ◽  
pp. 113851
Author(s):  
H. Dehestani ◽  
Y. Ordokhani
Keyword(s):  
Differential Equations ◽  
Efficient Approach ◽  
Hahn Polynomials

A MULTIPLE RICCATI EQUATIONS RATIONAL-EXPONENT METHOD AND ITS APPLICATION TO WHITHAM–BROER–KAUP EQUATION

2013 ◽  
Vol 27 (06) ◽  
pp. 1350014 ◽  
Author(s):  
QING LIU ◽  
ZI-HUA WANG ◽  
DONG-LI JIA
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Riccati Equation ◽  
Nonlinear Partial Differential Equations ◽  
Riccati Equations ◽  
Partial Differential ◽  
Efficient Approach ◽  
Generalized Riccati Equation

According to two dependent solutions to a generalized Riccati equation together with the equation itself, a multiple Riccati equations rational-exponent method is proposed and applied to Whitham–Broer–Kaup equation. It shows that this method is a more concise and efficient approach and can uniformly derive many types of combined solutions to nonlinear partial differential equations.

A discrete polynomials approach for optimal control of fractional Volterra integro-differential equations

2020 ◽  
pp. 107754632097115
Author(s):  
Fakhrodin Mohammadi ◽  
Leila Moradi ◽  
José António Tenreiro Machado
Keyword(s):  
Optimal Control ◽  
Differential Equations ◽  
Optimal Control Problems ◽  
Computational Cost ◽  
Control Problems ◽  
Operational Matrices ◽  
Hahn Polynomials ◽  
Discrete Norm ◽  
New Type ◽  
Discrete Polynomials

This study develops an efficient numerical method for optimal control problems governed by fractional Volterra integro-differential equations. A new type of polynomials orthogonal with respect to a discrete norm, namely discrete Hahn polynomials, is introduced and its properties investigated. Fractional operational matrices for the orthogonal polynomials are also derived. A direct numerical algorithm supported by the discrete Hahn polynomials and operational matrices is used to approximate solution of optimal control problems governed by fractional Volterra integro-differential equations. Several examples are analyzed and the results compared with those of other methods. The required CPU time assesses the computational cost and complexity of the proposed method.

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