Numerical algorithm for solving two-point, second-order periodic boundary value problems for mixed integro-differential equations

Arqub, Omar Abu; Al‐Smadi, Mohammed

doi:10.1016/j.amc.2014.06.063

Cited by 79 publications

(39 citation statements)

References 28 publications

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“…[16][17][18][19][20][21][22][23][24]). In [1], Henderson and Kunkel proved the uniqueness of solutions for the following linear differential equations with nonlocal boundary conditions: [3,4], Lin and Wu use the reproducing kernel to solve the following boundary value problems(BVPs).…”

Section: Introductionmentioning

confidence: 99%

Solving a class of linear nonlocal boundary value problems using the reproducing kernel

Wang

Tan

et al. 2015

Applied Mathematics and Computation

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Section: Introductionmentioning

confidence: 99%

Solving a class of linear nonlocal boundary value problems using the reproducing kernel

Wang

Tan

et al. 2015

Applied Mathematics and Computation

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“…All authors read and approved the final manuscript. 1 School of Mathematics and Statistics, Northeastern University at Qinhuangdao, Qinhuangdao, 066004, China.…”

Section: Competing Interestsmentioning

confidence: 99%

A modified kernel method for a time-fractional inverse diffusion problem

Liu¹,

Feng²

2015

Adv Differ Equ

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In this paper, we consider a time-fractional inverse diffusion problem, where the data is given at x = 1 and the solution is sought in the interval 0 ≤ x < 1. Such a problem is obtained from the classical diffusion equation by replacing the first-order time derivative by the Caputo fractional derivative of order α ∈ (0, 1). We show that a time-fractional inverse diffusion problem is severely ill-posed and we further apply a modified kernel method to solve it based on the solution in the frequency domain. The corresponding convergence estimates are provided. Finally, an example is constructed to show the feasibility and efficiency of the proposed method. MSC: 35R25; 35R30; 47A52

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“…For examples of these methods, we refer to the work in (Hesameddini and Fotros, 2012;Moaddy et al, 2011;Abdulaziz et al, 2008;Hashim et al, 2009;Odibat and Momani, 2006;Khalil et al, 2015a;2015b;2015c;El-Ajou et al, 2015;Abu-Gdairi et al, 2015;Freihat and Al-Smadi, 2013;Momani et al, 2014;Al-Smadi et al, 2013;. On the other hand, many applications for different problems by using other numerical algorithms can be found in (Abu Arqub et al, 2012;Abu Arqub and Al-Smadi, 2014;Moaddy et al, 2015;Komashynska and Al-Smadi, 2014;Komashynska et al, 2016).…”

Section: Introductionmentioning

confidence: 99%

Approximate Series Solution of Nonlinear, Fractional Klein-Gordon Equations Using Fractional Reduced Differential Transform Method

Abuteen¹,

Freihat²,

Al‐Smadi³

et al. 2016

Journal of Mathematics and Statistics

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This analysis proposes an analytical-numerical approach for providing solutions of a class of nonlinear fractional Klein-Gordon equation subjected to appropriate initial conditions in Caputo sense by using the Fractional Reduced Differential Transform Method (FRDTM). This technique provides the solutions very accurately and efficiently in convergent series formula with easily computable coefficients. The behavior of the approximate series solution for different values of fractional-order ߙ is shown graphically. A comparative study is presented between the FRDTM and Implicit Runge-Kutta approach to illustrate the efficiency and reliability of the proposed technique. Our numerical investigations indicate that the FRDTM is simple, powerful mathematical tool and fully compatible with the complexity of such problems.

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Numerical algorithm for solving two-point, second-order periodic boundary value problems for mixed integro-differential equations

Cited by 79 publications

References 28 publications

Solving a class of linear nonlocal boundary value problems using the reproducing kernel

Solving a class of linear nonlocal boundary value problems using the reproducing kernel

A modified kernel method for a time-fractional inverse diffusion problem

Approximate Series Solution of Nonlinear, Fractional Klein-Gordon Equations Using Fractional Reduced Differential Transform Method

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