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- Adomian decomposition method (1)
- Analytical scheme (1)
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- Caputo’s fractional derivative (1)
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- Differential equations (1)
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- Neutrosophic set; single-valued neutrosophic set; NS-cross entropy measure; multi-attribute group decision-making (1)
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- Numerical analysis (1)
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- Wealth inequality; financial stability; agent-based model; dynamical systems (1)
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Articles 1 - 5 of 5
Full-Text Articles in Special Functions
Fibonacci And Lucas Differential Equations, Esra Erkus-Duman, Hakan Ciftci
Fibonacci And Lucas Differential Equations, Esra Erkus-Duman, Hakan Ciftci
Applications and Applied Mathematics: An International Journal (AAM)
The second-order linear hypergeometric differential equation and the hypergeometric function play a central role in many areas of mathematics and physics. The purpose of this paper is to obtain differential equations and the hypergeometric forms of the Fibonacci and the Lucas polynomials. We also write again these polynomials by means of Olver’s hypergeometric functions. In addition, we present some relations between these polynomials and the other well-known functions.
Approximate Analytical Solutions Of Space-Fractional Telegraph Equations By Sumudu Adomian Decomposition Method, Hasib Khan, Cemil Tunç, Rahmat A. Khan, Akhtyar G. Shirzoi, Aziz Khan
Approximate Analytical Solutions Of Space-Fractional Telegraph Equations By Sumudu Adomian Decomposition Method, Hasib Khan, Cemil Tunç, Rahmat A. Khan, Akhtyar G. Shirzoi, Aziz Khan
Applications and Applied Mathematics: An International Journal (AAM)
The main goal in this work is to establish a new and efficient analytical scheme for space fractional telegraph equation (FTE) by means of fractional Sumudu decomposition method (SDM). The fractional SDM gives us an approximate convergent series solution. The stability of the analytical scheme is also studied. The approximate solutions obtained by SDM show that the approach is easy to implement and computationally very much attractive. Further, some numerical examples are presented to illustrate the accuracy and stability for linear and nonlinear cases.
Masked Instability: Within-Sector Financial Risk In The Presence Of Wealth Inequality, Youngna Choi
Masked Instability: Within-Sector Financial Risk In The Presence Of Wealth Inequality, Youngna Choi
Department of Applied Mathematics and Statistics Faculty Scholarship and Creative Works
We investigate masked financial instability caused by wealth inequality. When an economic sector is decomposed into two subsectors that possess a severe wealth inequality, the sector in entirety can look financially stable while the two subsectors possess extreme financially instabilities of opposite nature, one from excessive equity, the other from lack thereof. The unstable subsector can result in further financial distress and even trigger a financial crisis. The market instability indicator, an early warning system derived from dynamical systems applied to agent-based models, is used to analyze the subsectoral financial instabilities. Detailed mathematical analysis is provided to explain what financial …
Radial Basis Function Generated Finite Differences For The Nonlinear Schrodinger Equation, Justin Ng
Radial Basis Function Generated Finite Differences For The Nonlinear Schrodinger Equation, Justin Ng
Theses and Dissertations
Solutions to the one-dimensional and two-dimensional nonlinear Schrodinger (NLS) equation are obtained numerically using methods based on radial basis functions (RBFs). Periodic boundary conditions are enforced with a non-periodic initial condition over varying domain sizes. The spatial structure of the solutions is represented using RBFs while several explicit and implicit iterative methods for solving ordinary differential equations (ODEs) are used in temporal discretization for the approximate solutions to the NLS equation. Splitting schemes, integration factors and hyperviscosity are used to stabilize the time-stepping schemes and are compared with one another in terms of computational efficiency and accuracy. This thesis shows …
Ns-Cross Entropy-Based Magdm Under Single-Valued Neutrosophic Set Environment, Florentin Smarandache, Surapati Pramanik, Shyamal Dalapati, Shariful Alam, Tapan Kumar Roy
Ns-Cross Entropy-Based Magdm Under Single-Valued Neutrosophic Set Environment, Florentin Smarandache, Surapati Pramanik, Shyamal Dalapati, Shariful Alam, Tapan Kumar Roy
Branch Mathematics and Statistics Faculty and Staff Publications
A single-valued neutrosophic set has king power to express uncertainty characterized by indeterminacy, inconsistency and incompleteness. Most of the existing single-valued neutrosophic cross entropy bears an asymmetrical behavior and produces an undefined phenomenon in some situations. In order to deal with these disadvantages, we propose a new cross entropy measure under a single-valued neutrosophic set (SVNS) environment, namely NS-cross entropy, and prove its basic properties. Also we define weighted NS-cross entropy measure and investigate its basic properties. We develop a novel multi-attribute group decision-making (MAGDM) strategy that is free from the drawback of asymmetrical behavior and undefined phenomena. It is …