Quintic B-spline collocation method for fourth order partial integro-differential equations with a weakly singular kernel

Zhang, Haixiang; Han, Xuli; Yang, Xuehua

doi:10.1016/j.amc.2013.01.012

Cited by 34 publications

(27 citation statements)

References 32 publications

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“…As said in [41], the collocation method with B-spline approximations represents an economical alternative since it only requires the evaluation of the unknown parameters at the grid points. The quintic B-splines have been employed to solve Kuramoto-Sivashinsky equation [20], fourth order partial integro-differential equations [41], fourth-order parabolic partial differential equations [4] and second order mixed boundary value problem [17]. Also, there have been numerous applications of B-spline functions.…”

Section: Preliminary Results Of Quintic B-splinementioning

confidence: 99%

“…(40) and (41) gives N + 5 nonlinear algebraic equations which can be solved for the unknown coefficients c i by using an iterative method. Consequently, F (z) given in Eq.…”

Section: 1 Solution With the B-spline Methodsmentioning

confidence: 99%

“…Whittaker's cardinal series has played an extremely important role in the development of mathematical theory of sampling (e.g., see [39,40,41] and references therein). This series has been analyzed in depth in [19,34].…”

Section: A Survey Of Some Properties Of the Sinc Functionmentioning

confidence: 99%

See 2 more Smart Citations

Collocation method using quintic B-spline and sinc functions for solving a model of squeezing flow between two infinite plates

Saadatmandi

Asadi

Eftekhari

2015

International Journal of Computer Mathematics

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An axisymmetric viscous flow, generated by two large parallel plates slowly approaching each other is investigated. The steady nonlinear governing equations are converted into a fourth-order nonlinear differential equation using integrability condition. The resulting nonlinear boundary value problem is solved using quintic B-spline collocation and Sinc-collocation methods. The approach consists of reducing the problem to a set of algebraic equations. Numerical examples are included to demonstrate the validity and applicability of the techniques and a comparison is made with existing results in the literature.

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Section: Preliminary Results Of Quintic B-splinementioning

confidence: 99%

“…(40) and (41) gives N + 5 nonlinear algebraic equations which can be solved for the unknown coefficients c i by using an iterative method. Consequently, F (z) given in Eq.…”

Section: 1 Solution With the B-spline Methodsmentioning

confidence: 99%

See 1 more Smart Citation

Collocation method using quintic B-spline and sinc functions for solving a model of squeezing flow between two infinite plates

Saadatmandi

Asadi

Eftekhari

2015

International Journal of Computer Mathematics

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“…And the scheme was unconditional stable and convergent. Zhang et al [28] presented the quintic B-spline collocation method for fourth-order partial integro-differential equations with a weakly singular kernel. Ran and Zhang [16] formulated a new compact difference scheme for solving Equation (1.9) of the distributed order.…”

Section: Introductionmentioning

confidence: 99%

A compact finite difference scheme for the fourth‐order time‐fractional integro‐differential equation with a weakly singular kernel

Qiu

Guo

2019

Numerical Methods Partial

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In this paper, a compact finite difference scheme is constructed and investigated for the fourth-order time-fractional integro-differential equation with a weakly singular kernel. In the temporal direction, the Caputo derivative term is treated by means of L 1 discrete formula and the Riemann-Liouville fractional integral term is discretized by the second-order convolution quadrature rule. A fully discrete compact difference scheme is constructed with the space discretization by the fourth-order compact approximation. The stability and convergence are obtained by the discrete energy method, the Cholesky decomposition and the reduced-order method. Numerical experiments are presented to verify the theoretical analysis. KEYWORDSCholesky decomposition, compact difference scheme, fourth-order time-fractional integro-differential equation, second-order convolution quadrature rule, stability and convergence 1 Numer Methods Partial Differential Eq. 2020;36:439-458. wileyonlinelibrary.com/journal/num

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“…Zhang and Han [10] developed a quasi-wavelet-based numerical method for time-dependent fractional partial differential equation. Zhang et al [12] proposed quintic B-spline collocation method for the numerical solution of fourth-order partial integro-differential equations with a weakly singular kernel. Khan et al [4] used sextic spline solution for solving fourthorder parabolic partial differential equation.…”

Section: Introductionmentioning

confidence: 99%

Quintic B-spline method for time-fractional superdiffusion fourth-order differential equation

Arshed

2016

Math Sci

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The main objective of this paper is to obtain the approximate solution of superdiffusion fourth-order partial differential equations. Quintic B-spline collocation method is employed for fractional differential equations (FPDEs). The developed scheme for finding the solution of the considered problem is based on finite difference method and collocation method. Caputo fractional derivative is used for time fractional derivative of order a, 1\a\2. The given problem is discretized in both time and space directions. Central difference formula is used for temporal discretization. Collocation method is used for spatial discretization. The developed scheme is proved to be stable and convergent with respect to time. Approximate solutions are examined to check the precision and effectiveness of the presented method.

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Quintic B-spline collocation method for fourth order partial integro-differential equations with a weakly singular kernel

Cited by 34 publications

References 32 publications

Collocation method using quintic B-spline and sinc functions for solving a model of squeezing flow between two infinite plates

Collocation method using quintic B-spline and sinc functions for solving a model of squeezing flow between two infinite plates

A compact finite difference scheme for the fourth‐order time‐fractional integro‐differential equation with a weakly singular kernel

Quintic B-spline method for time-fractional superdiffusion fourth-order differential equation

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