A new quartic B-spline method for third–order self-adjoint singularly perturbed boundary value problems

Saini, Sonali; Mishra, Hradyesh Kumar

doi:10.12988/ams.2015.48654

Cited by 8 publications

(8 citation statements)

References 13 publications

(12 reference statements)

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“…The study also validates the theoretical results through numerical experiments and shows that the proposed algorithm has a faster rate of convergence in comparison to the new cubic B-spline collocation method [1] and uniform Haar wavelet resolution technique [2]. Moreover, the new method has an edge (in terms of accuracy) over other existing methods, when applied to the problems [3][4][5][6].…”

supporting

confidence: 71%

An efficient collocation algorithm for third order non-linear Emden–Fowler equation with multi-singularity

Alam,

Khan

2023

Preprint

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The study presents a novel algorithm for solving third order non-linear equations (Emden-Fowler type) with multi-singularity, which can be applied to various physical models. The algorithm uses a quintic trigonometric B-spline collocation method and a quasilinearization technique to avoid the non-linearity term in the equation. The study establishes a comprehensive error analysis for the proposed algorithm and proves that it has O(h4) convergence. The algorithm’s ability to handle singular behavior at the point ς = 0 and its faster rate of convergence exhibits a promising approach to solve such problems. The study also validates the theoretical results through numerical experiments and shows that the proposed algorithm has a faster rate of convergence in comparison to the new cubic B-spline collocation method [1] and uniform Haar wavelet resolution technique [2]. Moreover, the new method has an edge (in terms of accuracy) over other existing methods, when applied to the problems [3–6]. 2000 Mathematics Subject Classification: 65L80; 65M99; 65N35; 34B16; 65L05; 65L10; 65N55.

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supporting

confidence: 71%

An efficient collocation algorithm for third order non-linear Emden–Fowler equation with multi-singularity

Alam,

Khan

2023

Preprint

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“…However, they were able to show in general, that the accuracy of the scheme cannot be better than ) ( 2 h o . Moreover, (Saini and Mishra , 2015) presented an algorithm to develop approximate solution of third-order self-adjoint singularly perturbed two-point boundary value problem in which the highest order derivative is multiplied by a small parameter. First, they introduce the Quartic B-spline basis function, and then they use the linear sequence of Quartic B-spline to get the numerical solution of system of equations.…”

Section: *Corresponding Author: Gammeef@yahoocommentioning

confidence: 99%

Fourth-order stable central difference method for self-adjoint singular perturbation problems

Asrat¹,

File²,

Aga³

2016

Eth J Sci & Technol

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In this paper, fourth order stable central difference method is presented for solving self-adjoint singular perturbation problems for small values of perturbation parameter, ε . First, the given differential equation was reduced to its conventional form and then it was transformed into linear system of algebraic equations in the form of a three-term recurrence relation, which can easily be solved by using Thomas Algorithm. To validate the applicability of the method, four model examples have been solved for different values of perturbation parameter and mesh sizes. The numerical results are tabulated and compared with some of the previous findings reported in the literature and it is observed that the present method is more efficient. Graphs are also depicted in support of the numerical results. Both theoretical error bounds and numerical rate of convergence have been established for the method.

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“…Nowerdays many splines are known, including cubic, bicubic and biquadratic B-splines, trigonometric, orthogonal splines. Those splines are applied to the construction of curves and surfaces, for the designing of ship hulls, for the transformation of a sound signal's frequency [1,2,[6][7][8][10][11][12][13][14][15][16][17][18][19].…”

Section: Introductionmentioning

confidence: 99%

On approximations by polynomial and nonpolynomial integro-differential splines

Бурова¹,

Doronina²

2016

ams

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The present article is one of a number of articles in which the authors study the properties of integro-differential splines. The paper deals with the construction of integro-differential polynomial and nonpolynomial splines of the fifth order. The order of approximation with integrodifferential polynomial and nonpolynomial splines of the fifth order are given. We use the tensor product of polynomial and non-polynomial splines constructed in this paper for the approximation of functions of two variables. The results of these numerical experiments are given.

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A new quartic B-spline method for third–order self-adjoint singularly perturbed boundary value problems

Cited by 8 publications

References 13 publications

An efficient collocation algorithm for third order non-linear Emden–Fowler equation with multi-singularity

An efficient collocation algorithm for third order non-linear Emden–Fowler equation with multi-singularity

Fourth-order stable central difference method for self-adjoint singular perturbation problems

On approximations by polynomial and nonpolynomial integro-differential splines

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