Stochastic numerical approach for solving second order nonlinear singular functional differential equation

Sabir, Zulqurnain; Wahab, Hafiz Abdul; Umar, Muhammad; Erdoğan, Fevzi

doi:10.1016/j.amc.2019.124605

Cited by 57 publications

(33 citation statements)

References 46 publications

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“…Repeat the process by using the equations (20) and (25) for N � 6 and k � 0, 1, and 2. e solution of the obtained linear algebraic equations system is given as…”

Section: Resultsmentioning

confidence: 99%

“…e parameters τ i (i � 1, 2, 3, 4) and α, β, a, b, and c are the real constant values. e idea of the above model is achieved by extending the work of Sabir et al [25] that is used to explain the nonlinear singular FDEs of second order. For the verification and correctness of the designed MS-FDEs model, three different examples have been modeled and numerically solved by using the well-known differential transformation (DT) scheme, and the obtained numerical outcomes of DTscheme are compared with the exact solutions.…”

Section: Introductionmentioning

confidence: 99%

“…Some major key factors of the present study are summarized as follows: e mathematical modeled form of the third-order nonlinear MS-FDEs is presented successfully by extending the work of Sabir et al [25] e designed nonlinear MS-FDEs based on the designed model are addressed numerically by using the famous DT scheme.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

On a New Model Based on Third-Order Nonlinear Multisingular Functional Differential Equations

Sabir

Günerhan

Guirao

2020

Mathematical Problems in Engineering

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In this study, a novel mathematical model based on third-order nonlinear multisingular functional differential equations (MS-FDEs) is presented. e designed model is solved by using a well-known differential transformation (DT) scheme that is a very credible tool for solving the nonlinear third-order nonlinear MS-FDEs. In order to check the exactness, efficacy, and convergence of the scheme, some numerical examples are presented based on nonlinear third-order MS-FDEs and numerically solved by using DT scheme. e scheme of differential transformation allows us to find a complete solution and a closed approximate solution of the differential equation. e distinctive advantage of the computational technique is to deal with the complex and monotonous physical problems that are obtained in various branches of engineering and natural sciences. Moreover, a comparison of the obtained numerical outcomes from the exact solutions shows the correctness, accurateness, and exactness of the designed model as well as the presented scheme.

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“…Repeat the process by using the equations (20) and (25) for N � 6 and k � 0, 1, and 2. e solution of the obtained linear algebraic equations system is given as…”

Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

On a New Model Based on Third-Order Nonlinear Multisingular Functional Differential Equations

Sabir

Günerhan

Guirao

2020

Mathematical Problems in Engineering

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“…Researchers have widely studied the meta-heuristic based computing numerical approaches along with the neural network's strength for solving the linear/non-linear mathematical models [17][18][19][20][21][22][23][24]. Some recent applications of heuristic computing are corneal models for eye surgery [25], the non-linear Riccati system [26], the Bagley-Torvik system [27], non-linear systems of Bratu type [17], prey-predator non-linear models [28], nonlinear reactive transport models [29], non-linear optics models [30], non-linear singular functional differential models [31], singular non-linear systems arising in atomic physics [32], non-linear doubly singular systems [33], nanofluidic systems [34], micropolar fluid flow [35], the heartbeat model [36], the singular Lane-Emden equation based model [37], the heat conduction model of the human head [38], non-linear electric circuit models [39], finance [40], and mathematical models in Bioinformatics [41,42]. These influences proved the value, worth and consequence of the stochastic solvers based on robustness, accuracy and convergence.…”

Section: Introductionmentioning

confidence: 99%

A Neuro-Swarming Intelligence-Based Computing for Second Order Singular Periodic Non-linear Boundary Value Problems

et al. 2020

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In the present investigation, a novel neuro-swarming intelligence-based numerical computing solver is developed for solving second order non-linear singular periodic (NSP) boundary value problems (BVPs), i.e., NSP-BVPs, using the modeling strength of artificial neural networks (ANN) optimized with global search efficacy of particle swarm optimization (PSO) supported with the methodology of rapid local search by interior-point scheme (IPS), i.e., ANN-PSO-IPS. In order to check the proficiency, robustness, and stability of the designed ANN-PSO-IPS, two numerical problems of the NSP-BVPs have been presented for different numbers of neurons. The outcomes of the proposed ANN-PSO-IPS are compared with the available exact solutions to establish the worth of the solver in terms of accuracy and convergence, which is further endorsed through results of statistical performance metrics based on multiple implementations.

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“…e differential model has a broad application in many phenomena as in [12][13][14]. Recently, nonlinear fractional differential equations (NLFDEs) show significantly in engineering and applications of other sciences, for example, electrochemistry, physics, electromagnetics, and signal data processing [15][16][17][18][19][20][21][22].…”

Section: Introductionmentioning

confidence: 99%

Analytical Solutions for Nonlinear Dispersive Physical Model

Ali

Sadat

2020

Complexity

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Nonlinear evolution equations widely describe phenomena in various fields of science, such as plasma, nuclear physics, chemical reactions, optics, shallow water waves, fluid dynamics, signal processing, and image processing. In the present work, the derivation and analysis of Lie symmetries are presented for the time-fractional Benjamin–Bona–Mahony equation (FBBM) with the Riemann–Liouville derivatives. The time FBBM equation is reduced to a nonlinear fractional ordinary differential equation (NLFODE) using its Lie symmetries. These symmetries are derivations using the prolongation theorem. Applying the subequation method, we then use the integrating factor property to solve the NLFODE to obtain a few travelling wave solutions to the time FBBM.

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Stochastic numerical approach for solving second order nonlinear singular functional differential equation

Cited by 57 publications

References 46 publications

On a New Model Based on Third-Order Nonlinear Multisingular Functional Differential Equations

On a New Model Based on Third-Order Nonlinear Multisingular Functional Differential Equations

A Neuro-Swarming Intelligence-Based Computing for Second Order Singular Periodic Non-linear Boundary Value Problems

Analytical Solutions for Nonlinear Dispersive Physical Model

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