High-accuracy numerical scheme for solving the space-time fractional advection-diffusion equation with convergence analysis

Aghdam, Y. Esmaeelzade; Mesgarani, H.; Moremedi, G. M.; Khoshkhahtinat, M.

doi:10.1016/j.aej.2021.04.092

Cited by 14 publications

(2 citation statements)

References 21 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For some theoretical aspects of FDEs, one can refer to [35,36], while some practical applications of FDEs can be found in [37,38]. In the past years, many studies have been published on numerical methods for time and space FDEs; for example, see [39][40][41]. For some numerical algorithms that are employed to handle various types of FDEs, one can consult [42][43][44][45][46].…”

Section: Introductionmentioning

confidence: 99%

Eighth-Kind Chebyshev Polynomials Collocation Algorithm for the Nonlinear Time-Fractional Generalized Kawahara Equation

Abd-Elhameed,

Youssri,

Amin

et al. 2023

Fractal Fract

View full text Add to dashboard Cite

In this study, we present an innovative approach involving a spectral collocation algorithm to effectively obtain numerical solutions of the nonlinear time-fractional generalized Kawahara equation (NTFGKE). We introduce a new set of orthogonal polynomials (OPs) referred to as “Eighth-kind Chebyshev polynomials (CPs)”. These polynomials are special kinds of generalized Gegenbauer polynomials. To achieve the proposed numerical approximations, we first derive some new theoretical results for eighth-kind CPs, and after that, we employ the spectral collocation technique and incorporate the shifted eighth-kind CPs as fundamental functions. This method facilitates the transformation of the equation and its inherent conditions into a set of nonlinear algebraic equations. By harnessing Newton’s method, we obtain the necessary semi-analytical solutions. Rigorous analysis is dedicated to evaluating convergence and errors. The effectiveness and reliability of our approach are validated through a series of numerical experiments accompanied by comparative assessments. By undertaking these steps, we seek to communicate our findings comprehensively while ensuring the method’s applicability and precision are demonstrated.

show abstract

Section: Introductionmentioning

confidence: 99%

Eighth-Kind Chebyshev Polynomials Collocation Algorithm for the Nonlinear Time-Fractional Generalized Kawahara Equation

Abd-Elhameed,

Youssri,

Amin

et al. 2023

Fractal Fract

View full text Add to dashboard Cite

show abstract

“…Due to the above-mentioned properties, fractional order integral equations (FOIEs) have been used in many engineering and physics fields to investigate complex systems, for instance, viscoelasticity and traffic models, temperature and motor control, and solid mechanics [4][5][6][7][8]. However, FOIEs pose difficulties in achieving their accurate analytical solution and numerical techniques have to be used in order to derive useful result [9][10][11][12][13][14][15][16][17][18][19].…”

Section: Introductionmentioning

confidence: 99%

Hybridization of Block-Pulse and Taylor Polynomials for Approximating 2D Fractional Volterra Integral Equations

et al. 2022

View full text Add to dashboard Cite

This paper proposes an accurate numerical approach for computing the solution of two-dimensional fractional Volterra integral equations. The operational matrices of fractional integration based on the Hybridization of block-pulse and Taylor polynomials are implemented to transform these equations into a system of linear algebraic equations. The error analysis of the proposed method is examined in detail. Numerical results highlight the robustness and accuracy of the proposed strategy.

show abstract

On mild solutions of fractional impulsive differential systems of Sobolev type with fractional nonlocal conditions

Karthikeyan

Murugapandian²,

Hammouch

2022

Math Sci

View full text Add to dashboard Cite

High-accuracy numerical scheme for solving the space-time fractional advection-diffusion equation with convergence analysis

Cited by 14 publications

References 21 publications

Eighth-Kind Chebyshev Polynomials Collocation Algorithm for the Nonlinear Time-Fractional Generalized Kawahara Equation

Eighth-Kind Chebyshev Polynomials Collocation Algorithm for the Nonlinear Time-Fractional Generalized Kawahara Equation

Hybridization of Block-Pulse and Taylor Polynomials for Approximating 2D Fractional Volterra Integral Equations

On mild solutions of fractional impulsive differential systems of Sobolev type with fractional nonlocal conditions

Contact Info

Product

Resources

About