Differential quadrature solutions of eighth-order boundary-value differential equations

Liu, G. R.; Wu, T.Y.

doi:10.1016/s0377-0427(01)00577-5

Cited by 61 publications

(35 citation statements)

References 13 publications

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“…The first one is a generalization of periodic boundary value problem for impulsive eighth order differential equation. The studies on boundary value problems for eighth order differential equations have been made in [5,13]. The second one corrects a mistake occurred in a known published paper.…”

Section: Examplesmentioning

confidence: 96%

Solvability of impulsive periodic boundary value problems for higher order fractional differential equations

Liu

2016

Arab. J. Math.

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A class of periodic boundary value problems for higher order fractional differential equations with impulse effects is considered. We first convert the problem to an equivalent integral equation. Then, using a fixed-point theorem in Banach space, we establish existence results of solutions for this kind of boundary value problem for impulsive singular higher order fractional differential equations. Two examples are presented to illustrate the efficiency of the results obtained. Mathematics Subject Classification

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Section: Examplesmentioning

confidence: 96%

Solvability of impulsive periodic boundary value problems for higher order fractional differential equations

Liu

2016

Arab. J. Math.

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“…Watson and Scott [14] proved that Chow-Yorke algorithm was globally convergent for a class of spline collocation approximations to nonlinear two point boundary value problems. Liu and Wu [15] presented differential quadrature solutions of eighth-order differential equations. He [16,17,18,19,20] developed the variational iteration technique for solving non linear initial and boundary value problems.…”

Section: Introductionmentioning

confidence: 99%

Quartic B-Spline Collocation Method for Eighth Order Boundary Value Problems

Raju¹

2017

International Journal of Scientific and Innovative Mathematical

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“…al. [9] presented solution of special case of eighth order boundary value problems using variational iterational technique, Ghazala Akram and Hamood Ur Rehman [10] presented the solution of special case of eighth order boundary value problems using kernel space method there were used searching least square value method investigated for nonlinear eighth order boundary value problems, Liu and Wu [11] presented the solution of special case of eighth order boundary value problems using generalized differential quadrature rule, Koonprasert and Torvattanabum [12] presented variational iterational method for solving eighth order boundary value problems, Javidi and Golbai [13] presented HPM for solution of eighth order boundary value problems, Prorshouhi at. al.…”

Section: Introductionmentioning

confidence: 99%

Numerical Solution of Eighth Order Boundary Value Problems by Galerkin Method with Quintic B-splines

N.S.KasiViswanadham¹,

Ballem²

2014

IJCA

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In this paper, we present a finite element method involving Galerkin method with quintic B-splines as basis functions to solve a general eighth order two point boundary value problem.The basis functions are redefined into a new set of basis functions which vanish on the boundary where Dirichlet type of boundary conditions, Neumann boundary conditions, second order derivative boundary conditions and third order derivative type of boundary conditions are prescribed. The proposed method was applied to solve several examples of the eighth order linear and nonlinear boundary value problems. The solution of a nonlinear boundary value problem has been obtained as the limit of a sequence of solution of linear boundary value problems generated by quasilinearization technique. The obtained numerical results are compared with exact solutions available in the literature.

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Differential quadrature solutions of eighth-order boundary-value differential equations

Cited by 61 publications

References 13 publications

Solvability of impulsive periodic boundary value problems for higher order fractional differential equations

Solvability of impulsive periodic boundary value problems for higher order fractional differential equations

Quartic B-Spline Collocation Method for Eighth Order Boundary Value Problems

Numerical Solution of Eighth Order Boundary Value Problems by Galerkin Method with Quintic B-splines

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