Non-polynomial quintic spline for solving fourth-order fractional boundary value problems involving product terms

Khalid, Nauman; Abbas, Muhammad; Iqbal, Muhammad Kashif

doi:10.1016/j.amc.2018.12.066

Cited by 35 publications

(24 citation statements)

References 23 publications

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“…Various numerical methods based on spline functions have also been employed by researchers in pursue of reliable solutions for fractional-order differential equations [29][30][31]. The B-spline functions provide decent approximations in contrast with rest of numerical schemes due to the nominal, compact support and C 2 continuity [32].…”

Section: Introductionmentioning

confidence: 99%

A numerical algorithm based on modified extended B-spline functions for solving time-fractional diffusion wave equation involving reaction and damping terms

et al. 2019

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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.

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Section: Introductionmentioning

confidence: 99%

A numerical algorithm based on modified extended B-spline functions for solving time-fractional diffusion wave equation involving reaction and damping terms

et al. 2019

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“…where Ω α t y(z, t m+1 ) denotes the Caputo fractional time derivative approximation at t = t m+1 . Using (18), expression (20) takes the following form:…”

Section: Time Discretizationmentioning

confidence: 99%

“…In [17], Pezza and Pitolli used a fractional spline collocation Galerkin scheme to develop series solution for time fractional diffusion equation. Khalid et al [18] utilized the non-polynomial quintic spline collocation method to explore the numerical solution of fourth order fractional boundary value problem, involving product terms. In [19], Amin et al employed the quintic non-polynomial spline collocation scheme for solving time fractional fourth order PDEs.…”

Section: Introductionmentioning

confidence: 99%

A fourth order non-polynomial quintic spline collocation technique for solving time fractional superdiffusion equations

et al. 2019

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The purpose of this article is to present a technique for the numerical solution of Caputo time fractional superdiffusion equation. The central difference approximation is used to discretize the time derivative, while non-polynomial quintic spline is employed as an interpolating function in the spatial direction. The proposed method is shown to be unconditionally stable and O(h 4 + t 2 ) accurate. In order to check the feasibility of the proposed technique, some test examples have been considered and the simulation results are compared with those available in the existing literature.

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“…Khalid et al [35] proposed a numerical approach based on cubic modified extended basis spline functions for time fractional diffusion wave equations. The authors in [36] employed nonpolynomial quintic spline functions for numerical investigation of fourth-order fractional boundary value problems involving product terms.…”

Section: Introductionmentioning

confidence: 99%

A numerical investigation of Caputo time fractional Allen–Cahn equation using redefined cubic B-spline functions

et al. 2020

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We present a collocation approach based on redefined cubic B-spline (RCBS) functions and finite difference formulation to study the approximate solution of time fractional Allen-Cahn equation (ACE). We discretize the time fractional derivative of order α ∈ (0, 1] by using finite forward difference formula and bring RCBS functions into action for spatial discretization. We find that the numerical scheme is of order O(h 2 + t 2-α) and unconditionally stable. We test the computational efficiency of the proposed method through some numerical examples subject to homogeneous/nonhomogeneous boundary constraints. The simulation results show a superior agreement with the exact solution as compared to those found in the literature.

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Non-polynomial quintic spline for solving fourth-order fractional boundary value problems involving product terms

Cited by 35 publications

References 23 publications

A numerical algorithm based on modified extended B-spline functions for solving time-fractional diffusion wave equation involving reaction and damping terms

A numerical algorithm based on modified extended B-spline functions for solving time-fractional diffusion wave equation involving reaction and damping terms

A fourth order non-polynomial quintic spline collocation technique for solving time fractional superdiffusion equations

A numerical investigation of Caputo time fractional Allen–Cahn equation using redefined cubic B-spline functions

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