Solving linear and nonlinear fractional diffusion and wave equations by Adomian decomposition

Jafari, Hossein; Daftardar-Gejji, Varsha

doi:10.1016/j.amc.2005.12.031

Cited by 137 publications

(94 citation statements)

References 14 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…The results of the present technique have close agreement with approximate solutions obtained with the help of the Adomian decomposition method [8].…”

Section: Introductionsupporting

confidence: 74%

See 1 more Smart Citation

Numerical Solution of Nonlinear System of Partial Differential Equations by the Laplace Decomposition Method and the Pade Approximation

Mohamed¹,

Torky²

2013

AJCM

View full text Add to dashboard Cite

In this paper, Laplace decomposition method (LDM) and Pade approximant are employed to find approximate solutions for the Whitham-Broer-Kaup shallow water model, the coupled nonlinear reaction diffusion equations and the system of Hirota-Satsuma coupled KdV. In addition, the results obtained from Laplace decomposition method (LDM) and Pade approximant are compared with corresponding exact analytical solutions.

show abstract

“…The results of the present technique have close agreement with approximate solutions obtained with the help of the Adomian decomposition method [8].…”

Section: Introductionsupporting

confidence: 74%

“…n Also the linear and nonlinear terms i and is decomposed as an infinite series of Adomian polynomials (see [8,9]). Applying the inverse Laplace transform, finally we get…”

Section: Laplace Decomposition Methodsmentioning

confidence: 99%

Numerical Solution of Nonlinear System of Partial Differential Equations by the Laplace Decomposition Method and the Pade Approximation

Mohamed¹,

Torky²

2013

AJCM

View full text Add to dashboard Cite

show abstract

“…In other words, the ultimate behavior of the fractional system response must converge to the response of the integer order version of the equation. Some famous methods have been presented to approximate the analytical solution of linear/nonlinear differential equations (see, for example, [6] and [7]). Recently, the Laplace decomposition method has been suggested by Khuri. In [12,13], Khuri used Laplace transforms in ADM and approximated the solution of a class of differential equations.…”

Section: Introductionmentioning

confidence: 99%

Laplace homotopy perturbation method for Burgers equation with space- and time-fractional order

et al. 2016

View full text Add to dashboard Cite

Abstract:The fractional Burgers equation describes the physical processes of unidirectional propagation of weakly nonlinear acoustic waves through a gas-filled pipe. The Laplace homotopy perturbation method is discussed to obtain the approximate analytical solution of space-fractional and time-fractional Burgers equations. The method used combines the Laplace transform and the homotopy perturbation method. Numerical results show that the approach is easy to implement and accurate when applied to partial differential equations of fractional orders.

show abstract

“…In recent years, great interests were devoted to the analytical and numerical treatments of fractional differential equations. In general, fractional differential equations don't have exact solutions in closed forms, and therefore, numerical methods such as, the variational iteration [4], the homotopy analysis method [5], and the Adomian decomposition method [3,7,8], have been implemented for several types of fractional differential equations. Also, the maximum principle and the method of lower and upper solutions have been extended to deal with FDEs and obtain analytical and numerical results [6].…”

Section: Introductionmentioning

confidence: 99%

A Numerical method for solving a class of fractional Sturm-Liouville eigenvalue problems

Syam¹,

Al‐Mdallal²,

Al-Refai³

2017

Communications in Numerical Analysis

View full text Add to dashboard Cite

This article is devoted to both theoretical and numerical studies of eigenvalues of regular fractional 2α-order SturmLiouville problem where 1 2 < α ≤ 1. In this paper, we implement the reproducing kernel method RKM) to approximate the eigenvalues. To find the eigenvalues, we force the approximate solution produced by the RKM satisfy the boundary condition at x = 1. The fractional derivative is described in the Caputo sense. Numerical results demonstrate the accuracy of the present algorithm. In addition, we prove the existence of the eigenfunctions of the proposed problem. Uniformly convergence of the approximate eigenfunctions produced by the RKM to the exact eigenfunctions is proven.

show abstract

Solving linear and nonlinear fractional diffusion and wave equations by Adomian decomposition

Cited by 137 publications

References 14 publications

Numerical Solution of Nonlinear System of Partial Differential Equations by the Laplace Decomposition Method and the Pade Approximation

Numerical Solution of Nonlinear System of Partial Differential Equations by the Laplace Decomposition Method and the Pade Approximation

Laplace homotopy perturbation method for Burgers equation with space- and time-fractional order

A Numerical method for solving a class of fractional Sturm-Liouville eigenvalue problems

Contact Info

Product

Resources

About