A Numerical Algorithm Based on Modified Extended B-Spline Functions for Solving Time-Fractional Diffusion Wave Equation Involving Reaction and Damping Terms
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Date
2019
Journal Title
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Volume Title
Publisher
Springer
Open Access Color
GOLD
Green Open Access
No
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Top 10%
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Abstract
In this study, we have proposed an efficient numerical algorithm based on third degree modified extended B-spline (EBS) functions for solving time-fractional diffusion wave equation with reaction and damping terms. The Caputo time-fractional derivative has been approximated by means of usual finite difference scheme and the modified EBS functions are used for spatial discretization. The stability analysis and derivation of theoretical convergence validates the authenticity and effectiveness of the proposed algorithm. The numerical experiments show that the computational outcomes are in line with the theoretical expectations. Moreover, the numerical results are proved to be better than other methods on the topic.
Description
Abbas, Dr. Muhammad/0000-0002-0491-1528; Iqbal, Muhammad Kashif/0000-0003-4442-7498
Keywords
Time-Fractional Diffusion Wave Equation, Finite Difference Formulation, Caputo'S Time-Fractional Derivative, Modified Extended B-Spline Functions, Modified B-Spline Collocation Method, Economics, Structural engineering, Mathematical analysis, Finite difference formulation, Convergence Analysis of Iterative Methods for Nonlinear Equations, Differential equation, Engineering, Spline (mechanical), Modified extended B-spline functions, Numerical Methods for Singularly Perturbed Problems, B-spline, Machine learning, QA1-939, FOS: Mathematics, Reaction-Diffusion Equations, Stability (learning theory), Anomalous Diffusion Modeling and Analysis, Economic growth, Numerical Analysis, Time-Fractional Diffusion Equation, Modified B-spline collocation method, Fractional calculus, Partial differential equation, Applied mathematics, Computer science, Fractional Derivatives, Reaction–diffusion system, Modeling and Simulation, Physical Sciences, Convergence (economics), Fractional Calculus, Caputo’s time-fractional derivative, Finite Difference Schemes, Time-fractional diffusion wave equation, Mathematics, Ordinary differential equation, Discretization, Numerical analysis, Fractional derivatives and integrals, Caputo's time-fractional derivative, Finite difference methods for initial value and initial-boundary value problems involving PDEs, modified extended B-spline functions, finite difference formulation, modified B-spline collocation method, Fractional partial differential equations, time-fractional diffusion wave equation, Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
Fields of Science
01 natural sciences, 0103 physical sciences, 0101 mathematics
Citation
Khalid, Nauman...et al. (2019). "A numerical algorithm based on modified extended B-spline functions for solving time-fractional diffusion wave equation involving reaction and damping terms", Advances in Difference Equations, Vol. 2019, No. 1.
WoS Q
Q1
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OpenCitations Citation Count
23
Source
Advances in Difference Equations
Volume
2019
Issue
1
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CrossRef : 12
Scopus : 26
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Mendeley Readers : 9
SCOPUS™ Citations
28
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23
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9
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