Perturbed Collocation Method For Solving Singular Multi-order Fractional Differential Equations of Lane-Emden Type

Uwaheren, O. A.; Adebisi, A. F.; Taiwo, O. A.

doi:10.46481/jnsps.2020.69

Cited by 9 publications

(5 citation statements)

References 10 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…x 0 (x − t) y(t)dt+ We solve this problem at N = 4 and 5, however, make use of N = 4 for demonstration. Integral form of example 2 is x Exact N = 4 N = 5 0.2 -0.6400000000e-2 -0.6400000000e-2 -0.6400000000e-2 0.4 -0.3840000000e-1 -0.3840000000e-1 -0.3840000000e-1 0.6 -0.864000000e-1 -0.8640000000e-1 -0.8640000000e-1 0.8 -0.1024000000 -0.1024000000 -0.1024000000 1.0 -0.9000000000e-3 -0.900000000e-3 -0.900000000e-3 Using approximate solution (4) on (18) gives…”

Section: Examplementioning

confidence: 99%

“…Many different approaches have been adopted to investigate the solution of fractional integrodifferential equations, such as Adomian decompositions method [3][4][5], collocation method [6,7], Laplace decomposition method [8,9], Taylor expansion method [10], Least square method [9], differential transform method [11], homotopy perturbation method [12][13][14][15][16][17][18], sinc-collocation method [15][16][17] and variational iteration method [12,13].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Collocation Approach for the Computational Solution Of Fredholm-Volterra Fractional Order of Integro-Differential Equations

Ajileye

James

Abdullahi

et al. 2022

J. Nig. Soc. Phys. Sci.

View full text Add to dashboard Cite

In this work, a collocation technique is used to determine the computational solution to fractional order Fredholm-Volterra integro-differential equations with boundary conditions using Caputo sense. We obtained the linear integral form of the problem and transformed it into a system of linear algebraic equations using standard collocation points. The matrix inversion approach is adopted to solve the algebraic equation and substituted it into the approximate solution. We established the uniqueness and convergence of the method and some modelled numerical examples are provided to demonstrate the method’s correctness and efficiency. It is observed that the results obtained by our new method are accurate and performed better than the results obtained in the literature. The study will be useful to engineers and scientists. It is advantageous because it addresses the difficulty in tackling fractional order Fredholm-Volterra integro-differential problems using a simple collocation strategy. The approach has the advantage of being more accurate and reducing computer running time.

show abstract

Section: Examplementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Collocation Approach for the Computational Solution Of Fredholm-Volterra Fractional Order of Integro-Differential Equations

Ajileye

James

Abdullahi

et al. 2022

J. Nig. Soc. Phys. Sci.

View full text Add to dashboard Cite

show abstract

“…[1]. Some of the numerical solution of fractional differential equations developed in the literature include: Perturbed collocation method [2], Adomian decompositions method by [3][4][5], Collocation method by [6][7][8][9], Chebyshev-Gelerkin method [10], Bernoulli matrix method [11], Differential transform method [12], Pseudospectral method [13], Bernstein Polynomials method [14,15], the Mellin transform approach [16]. [17] utilized a numerical approach based on the boubaker polynomial to generate approximate numerical solutions to the multi-order fractional differential equations.…”

Section: Introductionmentioning

confidence: 99%

Collocation Method for the Numerical Solution of Multi-Order Fractional Differential Equations

Ajileye

James

2023

J. Nig. Soc. Phys. Sci.

View full text Add to dashboard Cite

This study presents a collocation approach for the numerical integration of multi-order fractional differential equations with initial conditions in the Caputo sense. The problem was transformed from its integral form into a system of linear algebraic equations. Using matrix inversion, the algebraic equations are solved and their solutions are substituted into the approximate equation to give the numerical results. The effectiveness and precision of the method were illustrated with the use of numerical examples.

show abstract

“…The results obtained showed that the technique has the capacity to yield good results with less computational time and memory space. Using Perturbed Collocation Method (PCM) [12] solved Singular Multi-order Fractional Differential Equations (SMFDE) of Lane-Emden Type with results which converged to the exact solutions. Akbari-Ganji Method (AGM) was used by [13], [14], [15] and [16] to find the numerical solution of differential equations arising from different physical problems.…”

Section: Introductionmentioning

confidence: 99%

Numerical Solution of Volterra Integro-Differential Equations by Akbari-Ganji’s Method

Uwaheren

Adebisi

Ishola

et al. 2022

BAREKENG: J. Math. & App.

Self Cite

View full text Add to dashboard Cite

In this study, Akbari-Ganji’s Method (AGM) was applied to solve Volterra Integro-Differential Difference Equations (VIDDE) using Legendre polynomials as basis functions. Here, a trial solution function of unknown constants that conform with the differential equations together with the initial conditions were assumed and substituted into the equations under consideration. The unknown coefficients are solved for using the new proposed approach, AGM which principally involves the application of the boundary conditions on successive derivatives and integrals of the problem to obtain a system of equations. The system of equation is solved using any appropriate computer software, Maple 18. Some examples were solved and the results compared to the exact solutions.

show abstract

Perturbed Collocation Method For Solving Singular Multi-order Fractional Differential Equations of Lane-Emden Type

Cited by 9 publications

References 10 publications

Collocation Approach for the Computational Solution Of Fredholm-Volterra Fractional Order of Integro-Differential Equations

Collocation Approach for the Computational Solution Of Fredholm-Volterra Fractional Order of Integro-Differential Equations

Collocation Method for the Numerical Solution of Multi-Order Fractional Differential Equations

Numerical Solution of Volterra Integro-Differential Equations by Akbari-Ganji’s Method

Contact Info

Product

Resources

About