Abstract
An effective algorithm for solving quadratic Riccati differential equation (QRDE), multipantograph delay differential equations (MPDDEs), and optimal control systems (OCSs) with pantograph delays is presented in this paper. This technique is based on Genocchi polynomials (GPs). The properties of Genocchi polynomials are stated, and operational matrices of derivative are constructed. A collocation method based on this operational matrix is used. The findings show that the technique is accurate and simple to use.
Highlights
Riccati differential equations (RDEs) play significant role in many fields of applied science [1].For example, a one-dimensional static Schrödinger equation [2,3,4]
The Bezier technique is utilized for solving Delay differential equations (DDEs) and switched systems
A new operational matrix of fractional order derivative based on Genocchi polynomials (GPs) is introduced to provide approximate solutions of multipantograph delay differential equations (MPDDEs) and optimal control systems with pantograph delays
Summary
Riccati differential equations (RDEs) play significant role in many fields of applied science [1]. A one-dimensional static Schrödinger equation [2,3,4]. The applications of this equation found in random processes, optimal control, and diffusion problems [1] and in stochastic realization theory, optimal control, network synthesis and financial mathematics. The method is very easy to utilize and straightforward, the obtained results are satisfactory (see the numerical results). The outline of this sequel is as follows: In Section 2, Some basic preliminaries are stated.
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