Adomian decomposition and homotopy perturbation method for the solution of time fractional partial integro-differential equations

Panda, A K; Santra, Sudarshan; Mohapatra, Jugal

doi:10.1007/s12190-021-01613-x

Cited by 24 publications

(9 citation statements)

References 42 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Lemma 2. For each m = 1, 2, … , M, the quantity T m, l defined in (11) satisfies the following inequality:…”

Section: Error Analysismentioning

confidence: 99%

“…For more details, one may refer to other studies [5][6][7][8][9] and references therein. Several analytical techniques are developed to solve linear as well as nonlinear FDEs such as Adomian decomposition method, [10][11][12][13] Homotopy perturbation method, [14][15][16] new iterative method, 17 variational iteration method, 18 and Laplace decomposition method. 19 Such methods do not need any discretization or approximation of the fractional derivatives.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Analysis of a finite difference method based on L1 discretization for solving multi‐term fractional differential equation involving weak singularity

Santra

Mohapatra

2022

Math Methods in App Sciences

Self Cite

View full text Add to dashboard Cite

In this article, we consider a multi‐term fractional initial value problem which has a weak singularity at the initial time t=0. The fractional derivatives are defined in Caputo sense. Due to such singular behavior, an initial layer occurs near t=0 which is sharper for small values of γ1 where γ1 is the highest order among all fractional differential operators. In addition, the analytical properties of the solution are provided. The classical L1 scheme is introduced on a uniform mesh to approximate the fractional derivatives. The error analysis is carried out, and it is shown that the numerical solution converges to the exact solution. Further analysis proves that the scheme is of order Ofalse(τγ1false) over the entire region, but it is of order O(τ) on any subdomain away from the origin. τ denotes the mesh parameter. To show the efficiency of the proposed scheme, this method is tested on several model problems, and the results are in agreement with the theoretical findings.

show abstract

“…Lemma 2. For each m = 1, 2, … , M, the quantity T m, l defined in (11) satisfies the following inequality:…”

Section: Error Analysismentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Analysis of a finite difference method based on L1 discretization for solving multi‐term fractional differential equation involving weak singularity

Santra

Mohapatra

2022

Math Methods in App Sciences

Self Cite

View full text Add to dashboard Cite

show abstract

“…To mention a few, Baranwal et al [17] developed an analytic algorithm based on the VIM and ADM methods for solving time fractional nonlinear type reaction-diffusion equations. Earlier studies [18,19] used the homotopy analysis method to solve time fractional nonlinear partial differential equation (PDE). Zhai et al [20] established an explicit spectral operator splitting framework for solving the fractional nonlocal Allen-Cahn model.…”

Section: Introductionmentioning

confidence: 99%

A novel numerical technique for solving time fractional nonlinear diffusion equations involving weak singularities

Ghosh

Mohapatra

2023

Math Methods in App Sciences

Self Cite

View full text Add to dashboard Cite

In this work, an efficient numerical approximation for the solution of the time fractional nonlinear diffuse interface model is studied. The solution to this problem has a weak singularity near the initial time t = 0. The fractional order nonlinear diffusion model is transformed into a system of nonlinear functional equations. The Daftardar-Gejji and Jafari method is employed to solve the corresponding nonlinear system. The L1 scheme is used to discretize the Caputo fractional derivative on a graded mesh in the time direction. In contrast, the spatial derivative is approximated by applying a classical central finite difference scheme to a uniform mesh. The convergence analysis and the error bounds are carried out. The analysis and the computational findings exhibit the effectiveness of the proposed method.

show abstract

“…He applied successfully this method to solve a variety of nonlinear equations in science and engineering [17][18][19]. Tis HPM has already been efectively employed by numerous researchers to resolve numerous linear and nonlinear issues such as solving heat radiation equations [20], KdV PDE studied by Ganji and Rafei [21], nonconservative oscillators [22], Laplace equation [23], time fractional partial integro-diferential equations [24], wave equations [25], heat conduction and convection equations [26], integral equations [27], couple spring mass system [28] and is also applicable in other areas [29][30][31]. He [32] applied HPM for solving Blasius diferential equation [33] and nonlinear boundary value problems.…”

Section: Introductionmentioning

confidence: 99%

Approximate Solutions of the Jet Engine Vibration Equation by the Homotopy Perturbation Method

Kawser

Alim

2022

Mathematical Problems in Engineering

View full text Add to dashboard Cite

In this paper, we consider the jet engine vibration system. With the help of the homotopy perturbation method (HPM), we solve the jet engine vibration (JEV) equation, which is a second-order nonlinear differential equation in the presence of damping and external forces. We compare the results with the corresponding numerical method to show the efficiency and reliability of this method. The findings demonstrate how well HPM works as a solution to these concerns, and it is anticipated that HPM will be used in a variety of new problems.

show abstract

Adomian decomposition and homotopy perturbation method for the solution of time fractional partial integro-differential equations

Cited by 24 publications

References 42 publications

Analysis of a finite difference method based on L1 discretization for solving multi‐term fractional differential equation involving weak singularity

Analysis of a finite difference method based on L1 discretization for solving multi‐term fractional differential equation involving weak singularity

A novel numerical technique for solving time fractional nonlinear diffusion equations involving weak singularities

Approximate Solutions of the Jet Engine Vibration Equation by the Homotopy Perturbation Method

Contact Info

Product

Resources

About