Haar wavelet collocation method for Lane–Emden equations with Dirichlet, Neumann and Neumann–Robin boundary conditions

In this paper, we have applied an iterative method to the singular and nonlinear fractional partial differential of Emden-Fowler equations types. Haar wavelets operational matrix of fractional integration will be used to solve the problem with the Picard technique. The singular equations turn to Sylvester equations that will be solved so that numerically solvable is very cost-effective. Moreover, the proposed technique is reliable enough to overcome the difficulty of the singular point at x = 0. Numerical examples are providing to illustrate the efficiency and accuracy of the technique.

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“…(29) for C r+1 and substituting in Eq. (20) or Eq. (26), we get the solution u r+1 at the collocation points.…”

Section: Methods Of Solutionmentioning

confidence: 99%

“…The wavelet algorithms for solving PDE (partial differential equation) are based on the Galerkin technique or the collocation method. Among them, the Haar wavelets consist of piecewise constant functions, and therefore, they are the simplest orthonormal wavelets with compact support [17,20].…”

Section: Introductionmentioning

confidence: 99%

Haar wavelet collocation method for solving singular and nonlinear fractional time-dependent Emden–Fowler equations with initial and boundary conditions

2019

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“…One of the most interesting approaches for numerical solution of fractional differential equations, which has drawn attention in recent years, is using wavelet functions . Wavelet theory is a new and developing field in mathematics and it has various applications in an extensive spectrum of engineering fields.…”

Section: Introductionmentioning

confidence: 99%

“…We will alternatively solve this equation using Radial basis functions and Jacobi spectral collocation methods, which are judged, and the results are far better than Zhang et al 28 One of the most interesting approaches for numerical solution of fractional differential equations, which has drawn attention in recent years, is using wavelet functions. 29,30 Wavelet theory is a new and developing field in mathematics and it has various applications in an extensive spectrum of engineering fields. Particularly, wavelets have been remarkably useful in analyzing signals for waveform representation and segmentations, the time frequency, and examining swift algorithms by an easy performance.…”

Section: Introductionmentioning

confidence: 99%

Numerical solution of variable fractional order advection‐dispersion equation using Bernoulli wavelet method and new operational matrix of fractional order derivative

et al. 2020

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In this article, the Bernoulli wavelet method is used to solve the space‐time variable fractional order advection‐dispersion equation. The equation contains Coimbra time fractional derivatives with variable order of γ1false(xfalse) as well as the Riemann‐Liouville space fractional derivatives with variable orders of γ2false(x,tfalse) and γ3false(x,tfalse). In fact, first, using the new operational matrices, we study the relationship between Bernoulli wavelets and piecewise functions. Then, according to the properties of piecewise functions and computing operational matrices of their fractional derivatives, we obtain operational matrices of the Bernoulli wavelet fractional derivatives. Using new operational matrices furnished from Caputo and Riemann‐Liouville and also suitable collocation points, the advection‐dispersion equation would be converted to a system of algebraic equations. Then, we would solve the equation numerically by utilizing a common method. Finally, the upper bound of the errors of the defined operational matrices and convergence analysis of the proposed method would be discussed. We would also reveal high accuracy of the method using some numerical samples.

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“…and presented many method as cubic spline method [1], cubic B-spline method [2], Hermite functions collocation method [3], homotopy perturbation method [4], Haar wavelet collocation method [5], the Variational iteration method [6].…”

Section: Introductionmentioning

confidence: 99%

A Novel Modification of Adomian Decomposition Method for Singular BVPs of Emden-Fowler Type

Alaqel

Hasan

2020

JAMCS

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In this paper, we apply a novel Modied of Adomian Decomposition Method (MADM) for solving Singular Boundary Value Problems (BVPs) of Emden-Fowler type of higher order. The higher-order Emden-Fowler equation is characterized by two types. In addition, we test the presented method by several linear and nonlinear examples, and compared the numerical result with the exact solution to illustrate performance and reliability of this method in nding approximate solutions as well as its successful in getting the complete solution in many case.

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Haar wavelet collocation method for Lane–Emden equations with Dirichlet, Neumann and Neumann–Robin boundary conditions

Cited by 80 publications

References 37 publications

Haar wavelet collocation method for solving singular and nonlinear fractional time-dependent Emden–Fowler equations with initial and boundary conditions

Haar wavelet collocation method for solving singular and nonlinear fractional time-dependent Emden–Fowler equations with initial and boundary conditions

Numerical solution of variable fractional order advection‐dispersion equation using Bernoulli wavelet method and new operational matrix of fractional order derivative

A Novel Modification of Adomian Decomposition Method for Singular BVPs of Emden-Fowler Type

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