An exponential spline technique for solving fractional boundary value problem

Akram, Ghazala; Tariq, Hira

doi:10.1007/s10092-015-0161-0

Cited by 12 publications

(11 citation statements)

References 17 publications

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“…, and u i-1 about the points x i in relations (12) using Taylor series respectively. Moreover, 2 12 u (4) i + h 4 360 u (6) i + 17h 6 60480 u (8) i…”

Section: Let Us Consider a Mesh With Nodal Pointsmentioning

confidence: 99%

“…Method IV. In this section, we would like to develop a numerical method based on the methods in references [4,25,29], and [28]. Also we investigate the convergence analysis of this method.…”

Section: The Weighted and Shifted Grünwald Difference Operator And Exmentioning

confidence: 99%

“…Also Adomian decomposition method for solving the initial value problem of Bagley-Torvik equation is discussed in [19], fractional linear multistep method and a predictor-corrector method of Adams type based on finite difference methods for initial value problem of Bagley-Torvik equation are discussed in [8]; Legendre operational matrix method for fractional differential equation is applied in [20]; and a combination of collocation points and first-order Bessel functions, which is called Bessel-collocation method for boundary value problem of Bagley-Torvik equation, is discussed in [27]. Quadratic spline solution for boundary value problem of fractional order is applied in [28], and an exponential spline technique for solving fractional boundary value problem is employed in [4]. The first aim of the present work is to explore exponential spline interpolation with multiple parameters and to produce the error of approximate exponential spline.…”

Section: Introductionmentioning

confidence: 99%

“…In Sect. 4, the numerical examples are given to illustrate the applications of the method, and also the computed results are compared with another known method in [4,9,17,21,28,29].…”

Section: Introductionmentioning

confidence: 99%

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An exponential spline approximation for fractional Bagley–Torvik equation

Emadifar

Jalilian

2020

Bound Value Probl

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In this paper, we approximate the solution of fractional Bagley-Torvik equation by using the exponential spline function and the shifted Grünwald difference operator. The proposed methods reduce to the system of algebraic equations. The convergence analysis of the methods has been discussed. The numerical examples are presented to illustrate the applications of the methods and to compare the computed results with the other methods.

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“…, and u i-1 about the points x i in relations (12) using Taylor series respectively. Moreover, 2 12 u (4) i + h 4 360 u (6) i + 17h 6 60480 u (8) i…”

Section: Let Us Consider a Mesh With Nodal Pointsmentioning

confidence: 99%

Section: The Weighted and Shifted Grünwald Difference Operator And Exmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…In Sect. 4, the numerical examples are given to illustrate the applications of the method, and also the computed results are compared with another known method in [4,9,17,21,28,29].…”

Section: Introductionmentioning

confidence: 99%

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An exponential spline approximation for fractional Bagley–Torvik equation

Emadifar

Jalilian

2020

Bound Value Probl

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“…The spline technique has been used extensively in the numerical solution of a variety of ordinary and partial differential equations . The quintic spline technique has numerous significant advantages over finite difference methods.…”

Section: Introductionmentioning

confidence: 99%

Quintic spline technique for time fractional fourth‐order partial differential equation

Tariq

Akram

2016

Numerical Methods Partial

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Higher order non‐Fickian diffusion theories involve fourth‐order linear partial differential equations and their solutions. A quintic polynomial spline technique is used for the numerical solutions of fourth‐order partial differential equations with Caputo time fractional derivative on a finite domain. These equations occur in many applications in real life problems such as modeling of plates and thin beams, strain gradient elasticity, and phase separation in binary mixtures, which are basic elements in engineering structures and are of great practical significance to civil, mechanical, and aerospace engineering. The quintic polynomial spline technique is used for space discretization and the time‐stepping is done using a backward Euler method based on the L1 approximation to the Caputo derivative. The stability and convergence analysis are also discussed. The numerical results are given, which demonstrate the effectiveness and accuracy of the numerical method. The numerical results obtained in this article are also compared favorably well with the results of (S. S. Siddiqi and S. Arshed, Int. J. Comput. Math. 92 (2015), 1496–1518). © 2016 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 445–466, 2017

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Convergence analysis of a second-order scheme for fractional differential equation with integral boundary conditions

Seal

Natesan

2022

J. Appl. Math. Comput.

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An exponential spline technique for solving fractional boundary value problem

Cited by 12 publications

References 17 publications

An exponential spline approximation for fractional Bagley–Torvik equation

An exponential spline approximation for fractional Bagley–Torvik equation

Quintic spline technique for time fractional fourth‐order partial differential equation

Convergence analysis of a second-order scheme for fractional differential equation with integral boundary conditions

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