Analysing time-fractional exotic options via efficient local meshless method

İnç, Mustafa; Khan, Muhammad Nawaz; Ahmad, Imtiaz; Yao, Shao-Wen; Ahmad, Hijaz; Thounthong, Phatiphat

doi:10.1016/j.rinp.2020.103385

Cited by 63 publications

(20 citation statements)

References 34 publications

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“…e implicit-difference scheme has been suggested for the solution of diffusion kinetic problem describing ion implantation by intermetallic phase formation. For further interesting models and methods, we refer the readers to [16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32]. We actually suggest a model of the surface modification of nickel-aluminum ions with the relaxation of mass flows.…”

Section: Discussionmentioning

confidence: 99%

Formation of Intermetallic Phases in Ion Implantation

Wang

Khan

Ayaz

et al. 2020

Journal of Mathematics

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This paper presents a model for the formation of intermetallic phases in the modified nickel ions in the surface layer of aluminum. It is shown that the absorption of ions in the bulk of the qualitative difference between the models with and without the relaxation of the mass flux is reduced to a difference in the characteristic scales. It was shown that the concentration distribution depends on the relation between time scales of various physical processes. We have extended the existing model to a unique simple model describing the formation of a new phase at the initial stage of ion implantation. The parameters containing in the model were evaluated using literature data. The known problem is a special case for our model.

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Section: Discussionmentioning

confidence: 99%

Formation of Intermetallic Phases in Ion Implantation

Wang

Khan

Ayaz

et al. 2020

Journal of Mathematics

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“…Thus, various vital approaches for determining the solutions of PDEs have been vastly suggested and presented. Among them, we mention the tanh-sech technique (Wazwaz, 2004), the Jacobi elliptic function approach (Dai & Zhang, 2006), (Zhang, Tong, & Wang, 2008), the exp-function approach (Aminikhad, Moosaei, & Hajipour, 2009), the sine-cosine approach (Wazwaz, 2005), the homogeneous balance technique (Fan & Zhang, 1998), the F-expansion approach (Zhang, Wang, Wang, & Fang, 2006), the extended tanh-method (Yang, Deng, & Wei, 2015), the Riccati-Bernoulli sub-ODE technique (Alharbi & Almatrafi, 2020c;Huang & Russell, 2011), the r-adaptive moving mesh strategy Budd, Huang, & Russell, 2009), the variational Iteration algorithm-I (Ahmad, Khan & Cesarano, 2019;, the variational iteration algorithm-II (Ahmad, Seadawy, Khan, & Thounthong, 2020;Bazighifan, Ahmad, &Yao, 2020), the Riccatti transformation method (Inc et al, 2020) and the meshless techniques (Ganji & Abdollahzadeh, 2008).…”

Section: Introductionmentioning

confidence: 99%

New exact and numerical solutions for the KdV system arising in physical applications

Almatrafi

Alharbi

Abdelrahman

2021

Arab Journal of Basic and Applied Sciences

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The Kortweg-de Vries (KdV) equation is more appropriate to simulate some natural phenomena and gives more accurate results for some physical systems such as the movement of water waves. In this work, novel analytical traveling wave solutions for a nonlinear KdV system are explored using the sech method. The exact solutions are presented in the form of hyperbolic functions. These solutions show the propagation of water waves on the surface. We also implement the numerical adaptive moving technique (MMPDEs) to construct the relevant system's numerical solutions. A detailed comparison between the numerical and analytical solutions is also presented to confirm the accuracy of the numerical technique. We present some new 2D and 3D figures to illustrate the behaviour of the exact and numerical solutions. The obtained numerical solutions verify the accuracy of the considered methods qualitatively and quantitatively. The stability of the obtained solutions is investigated using the Hamiltonian system. The achieved results can be applied for some new observations in the ocean, coastal water, macroscopic phenomena, and processes. The proposed techniques are potent tools to solve many other non-linear partial differential equations in applied mathematics.

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“…Partial derivatives provide a flexible model and an extraordinary tool for description of capturing the history of the variable and genetic characteristics of various dynamic systems. Extensive research has been carried out in the advancement of numerical and analytical solutions of linear and nonlinear FPDEs [1][2][3][4][5][6]. However, several researchers have not succeeded in deriving and modeling many complex phenomena utilizing linear or nonlinear PDEs with integer order [7].…”

Section: Introductionmentioning

confidence: 99%

Numerical Solution of the Multiterm Time‐Fractional Model for Heat Conductivity by Local Meshless Technique

et al. 2021

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Fractional partial differential equation models are frequently used to several physical phenomena. Despite the ability to express many complex phenomena in different disciplines, researchers have found that multiterm time-fractional PDEs improve the modeling accuracy for describing diffusion processes in contrast to the results of a single term. Nowadays, it attracts the attention of the active researchers. The aim of this work is concerned with the approximate numerical solutions of the three-term time-fractional Sobolev model equation using computationally attractive and reliable technique, known as a local meshless method. Because of the meshless character and the simple application in higher dimensions, there is a growing interest in meshless techniques. To assess the reliability and accuracy of the proposed method, three test problems and two types of irregular domains are taken into account.

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Analysing time-fractional exotic options via efficient local meshless method

Cited by 63 publications

References 34 publications

Formation of Intermetallic Phases in Ion Implantation

Formation of Intermetallic Phases in Ion Implantation

New exact and numerical solutions for the KdV system arising in physical applications

Numerical Solution of the Multiterm Time‐Fractional Model for Heat Conductivity by Local Meshless Technique

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