An O(h4) accurate cubic spline TAGE method for nonlinear singular two point boundary value problems

Mohanty, R. K.; Sachdev, P. L.; Jha, Navnit

doi:10.1016/j.amc.2003.08.145

Cited by 28 publications

(9 citation statements)

References 5 publications

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“…Based on previous study, they have discussed theoretically on how to compute the value of parameter r [5,6,[12][13][14]. In this paper, the optimum value of parameters 1 r and 2 r will be calculated by implementing several numerical experiment, so those optimum value will be found if the number of iteration is smaller.…”

Section: Two Parameter Alternating Group Explicit Iterative Methodsmentioning

confidence: 99%

Half-sweep two parameter alternating group explicit iterative method applied to fuzzy Poisson equation

Dahalan¹,

Sulaiman²

2016

ams

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Iterative methods particularly the Two Parameter Alternating Group Explicit (TAGE) methods are used to solve system of linear equations generated from the discretization of two-point fuzzy boundary value problems (FBVPs). The formulation and implementation of the Full-Sweep TAGE (FSTAGE) and Half-Sweep TAGE (HSTAGE) methods are also presented. Then numerical experiments are carried out onto two example problems to verify the effectiveness of the method. The results show that TAGE method is superior compare to AGE method in the aspect of number of iterations, execution time and Hausdorff distance.

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Section: Two Parameter Alternating Group Explicit Iterative Methodsmentioning

confidence: 99%

Half-sweep two parameter alternating group explicit iterative method applied to fuzzy Poisson equation

Dahalan¹,

Sulaiman²

2016

ams

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“…Ravi Kanth and Reddy [40,41] studied a particular singular BVP u (x) + (k/x)u (x) + q(x)u(x) = r(x) by applying higher-order finite difference method and cubic spline method. Mohan and his co-workers considered such a singular BVP u (x) + (a/x)u (x) + (a/x 2 )u(x) = r(x) using a fourth-order accurate cubic spine method [37]. Cui and Geng present an reproducing kernel Hilbert space method (RKHSM) for a class of linear singular BVPs [8].…”

Section: Introductionmentioning

confidence: 99%

Solving singular nonlinear boundary value problems by combining the homotopy perturbation method and reproducing kernel Hilbert space method

Geng

Cui

2010

International Journal of Computer Mathematics

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This paper investigates singular nonlinear boundary value problems (BVPs). The numerical solutions are developed by combining He's homotopy perturbation method (HPM) and reproducing kernel Hilbert space method (RKHSM). He's HPM is based on the use of traditional perturbation method and homotopy technique. The HPM can reduce a nonlinear problem to a sequence of linear problems and generate a rapid convergent series solution in most cases. RKHSM is also an analytical technique, which can solve powerfully singular linear BVPs. Therefore, we solve singular nonlinear BVPs using advantages of these two methods. Three numerical examples are presented to illustrate the strength of the method.

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“…Kanth and Reddy solved a particular singular boundary value problem by applying higher order finite difference method [2].The same authors investigated by using the cubic spline [3] method. Mohanty et al [4] introduced accurate cubic spline method for solving the singular boundary value problems. Variational iteration method (VIM) was introduced by Wazwaz [5] for solving nonlinear singular boundary value problems.…”

Section: Introductionmentioning

confidence: 99%

A computational method for solving a class of singular boundary value problems arising in science and engineering

Pirabaharan

Chandrakumar²

2016

Egyptian Journal of Basic and Applied Sciences

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A B S T R A C TThis note deals with a new computational method for solving a class of singular boundary value problems. The method is based upon Bernstein Polynomials. The properties of Bernstein Polynomials, together with Bernstein operational matrix for differentiation formula, are presented and utilized to reduce the given singular boundary value problems to the set of algebraic equations. The proposed method is applied to solve some test problems with the comparison between the computational solutions and the exact solutions. The results indicate that the proposed algorithm provides high reliability and good accuracy.

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An O(h4) accurate cubic spline TAGE method for nonlinear singular two point boundary value problems

Cited by 28 publications

References 5 publications

Half-sweep two parameter alternating group explicit iterative method applied to fuzzy Poisson equation

Half-sweep two parameter alternating group explicit iterative method applied to fuzzy Poisson equation

Solving singular nonlinear boundary value problems by combining the homotopy perturbation method and reproducing kernel Hilbert space method

A computational method for solving a class of singular boundary value problems arising in science and engineering

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