☆ 4.5 Article

Investigation of Fractional Nonlinear Regularized Long-Wave Models via Novel Techniques

SYMMETRY-BASEL (2023)

Related references

Note: Only part of the references are listed.

Article Engineering, Electrical & Electronic

A linear AC unit commitment formulation: An application of data-driven linear power flow model

Zhentong Shao et al.

Summary: This paper proposes a linear AC unit commitment model to solve the intractable large-scale non-convex and nonlinear AC unit commitment problem. By adopting data-driven linear power flow model and chance-constrained support vector regression, a high-accuracy solution close to the exact AC unit commitment is obtained, and physical models are used to deduce aid formulations to make the model more robust.

INTERNATIONAL JOURNAL OF ELECTRICAL POWER & ENERGY SYSTEMS (2023)

Add to Collection

Article Mathematics, Applied

Fitted modifications of Runge-Kutta-Nystrom pairs of orders 7(5) for addressing oscillatory problems

Vladislav N. Kovalnogov et al.

Summary: A recently discovered 7(5) order Runge-Kutta-Nystrom pair method with six stages per step has been modified by adjusting four of its weights. The modified method can exactly integrate the harmonic oscillator equation without order reduction typically associated with such modifications. Numerical results obtained using the standard six stages pairs support the effectiveness of our modified method.

MATHEMATICAL METHODS IN THE APPLIED SCIENCES (2023)

Add to Collection

Article Acoustics

Radial basis functions based meshfree schemes for the simulation of non-linear extended Fisher-Kolmogorov model

Sanjay Kumar et al.

Summary: This work presents two radial basis functions (RBFs) based meshfree schemes for numerically simulating nonlinear extended Fisher-Kolmogorov model. The schemes approximate time and spatial derivatives using different methods and validate effectiveness through stability analysis.

WAVE MOTION (2022)

Add to Collection

Article Acoustics

Local radial basis functions and scale-3 Haar wavelets operational matrices based numerical algorithms for generalized regularized long wave model

Sapna Pandit

Summary: Two numerical algorithms are developed in this article to simulate the generalized regularized long wave (GRLW) model using local radial basis functions (LRBFs) and Scale 3 Haar wavelets (S3HWs). The well-posedness of the model is discussed, and the semi-discrete and fully discretized models are analyzed for truncation errors, stability, and simulation results.

WAVE MOTION (2022)

Add to Collection

Article Mathematics, Applied

Analytical investigation of fractional-order Newell-Whitehead-Segel equations via a novel transform

Mounirah Areshi et al.

Summary: In this paper, two different methods are used to find the solution of the time-fractional Newell-Whitehead-Segel equation, which plays an efficient role in describing stripe patterns in nonlinear systems. The proposed methods provide numerical results that are in strong agreement with an exact solution, and the effectiveness of these methods is demonstrated through graphs and tables. Furthermore, the results show that the solution approaches the exact solution as the fractional order tends towards an integer order. The proposed methods are interesting, easy to use, and highly accurate for solving various nonlinear fractional-order partial differential equations.

AIMS MATHEMATICS (2022)

Add to Collection

Article Mathematics, Applied

New family for Runge-Kutta-Nystrom pairs of orders 6(4) with coefficients trained to address oscillatory problems

Vladislav N. Kovalnogov et al.

Summary: This paper presents a new method for solving special second-order initial value problems and validates its effectiveness through extensive numerical testing.

MATHEMATICAL METHODS IN THE APPLIED SCIENCES (2022)

Add to Collection

Article Mathematics

Analytical Investigation of Fractional-Order Cahn-Hilliard and Gardner Equations Using Two Novel Techniques

Mohammed Kbiri Alaoui et al.

Summary: In this paper, we used the natural decomposition approach with non-singular kernel derivatives to find the solution to nonlinear fractional Gardner and Cahn-Hilliard equations. The proposed methods were compared with exact solutions and other methods, showing accuracy and validity.

MATHEMATICS (2022)

Add to Collection

Article Engineering, Chemical

A Robust Hammerstein-Wiener Model Identification Method for Highly Nonlinear Systems

Lijie Sun et al.

Summary: A robust Hammerstein-Wiener model identification method is proposed in this paper for highly nonlinear systems using a small and noisy data set. By using parsimonious parametrization models and an iteration method, the proposed method can improve the accuracy and variance of parameter estimation compared to over-parametrization model based methods.

PROCESSES (2022)

Add to Collection

Article Multidisciplinary Sciences

Fractional View Analysis of Kuramoto-Sivashinsky Equations with Non-Singular Kernel Operators

Azzh Saad Alshehry et al.

Summary: In this article, the authors investigate the Kuramoto-Sivashinsky equation, a nonlinear model describing various physical and chemical phenomena. They propose a novel technique called the natural decomposition method, combined with fractional derivatives, to obtain an approximate analytical solution for this equation. The results show that this method is efficient, simple, and accurate in studying nonlinear models in science and technology.

SYMMETRY-BASEL (2022)

Add to Collection

Article Chemistry, Multidisciplinary

An Improved Algorithm of Drift Compensation for Olfactory Sensors

Siyu Lu et al.

Summary: This research focuses on the semi-supervised learning algorithm for different domain data in machine olfaction, aiming to address the issue of sensor drift. A novel algorithm, DTSWKELM, is proposed to transform the data through domain transformation and solve the semi-supervised classification problem of different domain data as a problem of the same domain data.

APPLIED SCIENCES-BASEL (2022)

Add to Collection

Article Chemistry, Multidisciplinary

A Semi-Supervised Extreme Learning Machine Algorithm Based on the New Weighted Kernel for Machine Smell

Wei Dang et al.

Summary: Machine sense of smell plays an important role in various scenarios, but it relies on data and algorithms for support. This study proposes a semi-supervised extreme learning machine algorithm, SELMWK, which combines weighted kernel with SKELM to handle a small amount of labeled data and a large amount of unlabeled data, achieving good classification performance.

APPLIED SCIENCES-BASEL (2022)

Add to Collection

Article

Solitary Wave Propagation of the Generalized Kuramoto-Sivashinsky Equation in Fragmented Porous Media

M. N. Rasoulizadeh et al.

International Journal of Applied and Computational Mathematics (2022)

Add to Collection

Article Mathematics, Applied

Evaluation of time-fractional Fisher's equations with the help of analytical methods

Ahmed M. Zidan et al.

Summary: This article demonstrates the solution to the time-fractional Fisher's equation using two well-known analytical methods. The proposed techniques, a modified form of the Adomian decomposition method and homotopy perturbation method with a Yang transform, show high accuracy and reliability through illustrative examples. The benefits of these techniques include a small number of calculations and applicability in various fields of applied sciences.

AIMS MATHEMATICS (2022)

Add to Collection

Article Mathematical & Computational Biology

Efficient algorithms for scheduling equal-length jobs with processing set restrictions on uniform parallel batch machines

Shuguang Li

Summary: This article discusses the problem of scheduling jobs with equal lengths on uniform parallel batch machines with non-identical capacities. It presents efficient exact algorithms for different objective functions and makespan minimization in cases of equal and unequal release times.

MATHEMATICAL BIOSCIENCES AND ENGINEERING (2022)

Add to Collection

Article Mathematics, Interdisciplinary Applications

Multi-AUV Dynamic Maneuver Countermeasure Algorithm Based on Interval Information Game and Fractional-Order DE

Lu Liu et al.

Summary: This paper proposes a multi-AUV dynamic maneuver countermeasure algorithm based on interval information game theory and fractional-order Differential Evolution (DE) to address the challenges posed by the instability of the underwater environment and underwater communication. By establishing advantage function, payoff matrix and Nash equilibrium condition, and utilizing the fractional-order DE algorithm to determine the optimal strategy, the superiority of the algorithm is verified through an example.

FRACTAL AND FRACTIONAL (2022)

Add to Collection

Article Mathematics, Applied

On the solution of fractional modified Boussinesq and approximate long wave equations with non-singular kernel operators

Thongchai Botmart et al.

Summary: In this paper, the Natural decomposition approach and nonsingular kernel derivatives were used to explore the modified Boussinesq and approximate long wave equations. Convergence analysis, error analysis, and verification of the approach were performed. The results show that the suggested scheme is computationally accurate and effective in solving fractional coupled nonlinear complicated phenomena.

AIMS MATHEMATICS (2022)

Add to Collection

Article Computer Science, Interdisciplinary Applications

Numerical solution of singular boundary value problems using advanced Adomian decomposition method

Umesh et al.

Summary: In this work, a powerful method for solving non-linear singular boundary value problems, known as the advanced Adomian decomposition method, is introduced. This method discusses the use of boundary conditions to obtain coefficient of approximate series solution, provides convergence analysis, error bound, and illustrates high precision approximations with a large effective region of convergence. Examples are considered to demonstrate the robustness and effectiveness of the proposed method.

ENGINEERING WITH COMPUTERS (2021)

Add to Collection

Article Mathematics, Applied

Analysis and numerical computations of the fractional regularized long-wave equation with damping term

Mehmet Yavuz et al.

Summary: This study examines the existence and uniqueness of solutions to the fractional damped generalized regularized long-wave equation using the fixed-point theorem in the Atangana-Baleanu fractional derivative. The modified Laplace decomposition method is utilized to obtain approximate-analytical solutions for the nonlinear model, while numerical simulations are performed with different values of the fractional parameter to observe the effects of various parameters and variables on displacement.

MATHEMATICAL METHODS IN THE APPLIED SCIENCES (2021)

Add to Collection

Article Mathematics, Interdisciplinary Applications

Analytical Investigation of Noyes-Field Model for Time-Fractional Belousov-Zhabotinsky Reaction

Mohammed Kbiri Alaoui et al.

Summary: In this article, the solution of the time-fractional Belousov-Zhabotinskii reaction is found using modified Adomian decomposition method and homotopy perturbation method with Yang transform. The obtained solution is in series form, which helps in investigating the analytical solution of the system. The proposed methods are verified for accuracy through an illustrative example and comparison with graphs, showing the desired rate of convergence to the exact solution. The technique's primary benefit lies in its low computational requirements and applicability to various domains.

COMPLEXITY (2021)

Add to Collection

Article Engineering, Multidisciplinary

An efficient local meshless method for the equal width equation in fluid mechanics

M. N. Rasoulizadeh et al.

Summary: The paper presents an accurate and robust meshless approach for solving the nonlinear equal width equation, using localized radial basis function-finite difference method and implicit techniques. The stability analysis and comparison with other techniques are also conducted to assess the validity, efficiency, and accuracy of the method.

ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS (2021)

Add to Collection

Article Engineering, Mechanical

Dark and bright soliton solutions and computational modeling of nonlinear regularized long wave model

Sanjay Kumar et al.

Summary: The authors in this article simulated and studied dark and bright soliton solutions of 1D and 2D regularized long wave (RLW) models. They used the tanh-coth method to obtain soliton solutions and developed a meshfree method for computational modeling. The stability of the method was discussed using matrix technique, and numerical experiments were conducted to verify the effectiveness and integrity of the developed approach.

NONLINEAR DYNAMICS (2021)

Add to Collection

Article Engineering, Mechanical

Soliton solutions of the nonlinear sine-Gordon model with Neumann boundary conditions arising in crystal dislocation theory

O. Nikan et al.

Summary: This paper presents an efficient and accurate localized meshless collocation method for solving the nonlinear sine-Gordon equation with Neumann boundary conditions, demonstrating stability and convergence. The proposed LRBF-PU technique shows advantages in computational efficiency and well-conditioned linear systems compared to global collocation methods. Numerical results validate the method's effectiveness in capturing ring and line solitons of circular and elliptic shapes, with good agreement compared to existing literature.

NONLINEAR DYNAMICS (2021)

Add to Collection

Article Multidisciplinary Sciences

Numerical Investigation of Fractional-Order Swift-Hohenberg Equations via a Novel Transform

Kamsing Nonlaopon et al.

Summary: The Elzaki transform decomposition method was implemented to solve time-fractional Swift-Hohenberg equations in this paper, related to temperature and thermal convection in fluid dynamics. The Caputo manner was used to describe fractional derivatives. The method is easy to implement, requires few calculations, and has been validated through numerical examples. Illustrative figures were used to verify the analytical schemes for fractional-order problems proposed in the study.

SYMMETRY-BASEL (2021)

Add to Collection

Article Mathematics, Applied

The impact of LRBF-FD on the solutions of the nonlinear regularized long wave equation

M. N. Rasoulizadeh et al.

Summary: This paper develops a method for the numerical solution of the nonlinear regularized long wave equation, discretizing the unknown solution through time and spatial discretization, and addressing the ill-conditioning problem derived from global collocation methods.

MATHEMATICAL SCIENCES (2021)

Add to Collection

Article Engineering, Multidisciplinary

New exact solutions for time-fractional Kaup-Kupershmidt equation using improved (G′/G)-expansion and extended (G′/G)-expansion methods

S. Sahoo et al.

ALEXANDRIA ENGINEERING JOURNAL (2020)

Add to Collection

Article Mathematics, Applied

Nonlinear regularized long-wave models with a new integral transformation applied to the fractional derivative with power and Mittag-Leffler kernel

Mehmet Yavuz et al.

ADVANCES IN DIFFERENCE EQUATIONS (2020)

Add to Collection

Article Mathematics, Applied

An approximate analytical solution of the Navier-Stokes equations within Caputo operator and Elzaki transform decomposition method

Hajira et al.

ADVANCES IN DIFFERENCE EQUATIONS (2020)

Add to Collection

Article Thermodynamics

NUMERICAL COMPUTATION OF THE TIME NON-LINEAR FRACTIONAL GENERALIZED EQUAL WIDTH MODEL ARISING IN SHALLOW WATER CHANNEL

Nguyen Huu Can et al.

THERMAL SCIENCE (2020)

Add to Collection

Article Engineering, Marine

An efficient analytical technique for fractional partial differential equations occurring in ion acoustic waves in plasma

Amit Goswami et al.

JOURNAL OF OCEAN ENGINEERING AND SCIENCE (2019)

Add to Collection

Article Engineering, Mechanical

A Numerical Algorithm to Capture Spin Patterns of Fractional Bloch Nuclear Magnetic Resonance Flow Models

R. C. Mittal et al.

JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS (2019)

Add to Collection

Article Physics, Multidisciplinary

Analysis of regularized long-wave equation associated with a new fractional operator with Mittag-Leffler type kernel

Devendra Kumar et al.

PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS (2018)

Add to Collection

Article Computer Science, Interdisciplinary Applications

Quasilinearized Scale-3 Haar wavelets-based algorithm for numerical simulation of fractional dynamical systems

R. C. Mittal et al.

ENGINEERING COMPUTATIONS (2018)

Add to Collection

Article Mathematics, Applied

Optimal existence and uniqueness theory for the fractional heat equation

Matteo Bonforte et al.

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS (2017)

Add to Collection

Article Engineering, Electrical & Electronic

New solutions for conformable fractional Nizhnik-Novikov-Veselov system via G'/G expansion method and homotopy analysis methods

A. Kurt et al.

OPTICAL AND QUANTUM ELECTRONICS (2017)

Add to Collection

Article Computer Science, Interdisciplinary Applications

Bat inspired algorithm for discrete size optimization of steel frames

O. Hasancebi et al.

ADVANCES IN ENGINEERING SOFTWARE (2014)

Add to Collection

Article Mathematics, Applied

Existence Results for Solutions of Nonlinear Fractional Differential Equations

Ali Yakar et al.

ABSTRACT AND APPLIED ANALYSIS (2012)

Add to Collection

Article Mathematics, Applied

From Newton's Equation to Fractional Diffusion and Wave Equations

Luis Vazquez

ADVANCES IN DIFFERENCE EQUATIONS (2011)

Add to Collection

Article Mathematics, Applied

Projective synchronization of chaotic fractional-order energy resources demand-supply systems via linear control

Baogui Xin et al.

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION (2011)

Add to Collection

Article Computer Science, Interdisciplinary Applications

Fractional differential equations in electrochemistry

Keith B. Oldham

ADVANCES IN ENGINEERING SOFTWARE (2010)

Add to Collection

Article Mathematics, Applied

The first integral method for modified Benjamin-Bona-Mahony equation

S. Abbasbandy et al.

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION (2010)

Add to Collection

Article Mathematics, Applied

Fractional calculus models of complex dynamics in biological tissues

Richard L. Magin

COMPUTERS & MATHEMATICS WITH APPLICATIONS (2010)

Add to Collection

Article Automation & Control Systems

Robust H∞ tracking control of boiler-turbine systems

J. Wu et al.

ISA TRANSACTIONS (2010)

Add to Collection

Article Mathematics, Applied

On the fractional-order logistic equation

A. M. A. El-Sayed et al.

APPLIED MATHEMATICS LETTERS (2007)

Add to Collection

Article Physics, Multidisciplinary

On fractional order differential equations model for nonlocal epidemics

E. Ahmed et al.

PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS (2007)

Add to Collection

Article Physics, Multidisciplinary

The first-integral method to study the Burgers-Korteweg-de Vries equation

ZS Feng

JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL (2002)

Add to Collection

Article Physics, Multidisciplinary

Fractional market dynamics

N Laskin

PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS (2000)

Add to Collection

Article Mechanics

A coupling method of a homotopy technique and a perturbation technique for non-linear problems

JH He

INTERNATIONAL JOURNAL OF NON-LINEAR MECHANICS (2000)

Add to Collection

© Peeref 2019-2024. All rights reserved.