B‐spline collocation methods for numerical solutions of the Burgers′ equation

Dağ, İdris; Irk, Dursun; Şahin, Ali

doi:10.1155/mpe.2005.521

Cited by 46 publications

(34 citation statements)

References 13 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…After the error concentration have been determined over the problem domain, selection of the mesh parameter s , 1 is done over the interval ½0:9; 1 with the increment 0:0001 to find the least error. Comparison of results with the case of s ¼ 1, the best parameter of s in the domain interval and those referenced in the paper (Dag et al (2005) and Ali et al (1992)) are presented in Table II. In Figures 6-8 error distributions of the both schemes at times t ¼ 1:7; t ¼ 2:5 and t ¼ 3:25 are plotted for both uniform and graded meshes together.…”

Section: Numerical Examplesmentioning

confidence: 99%

“…Table I. At different times, L 1 £ 10 3 errors for n ¼ 0:005 and Dt ¼ 0:01 (Dag et al, 2005) 13.8155 16.7712 13.8155 CBCM (Dag et al, 2005) 27 (Dag et al, 2005) 13.8155 16.7712 13.8155 CBCM (Dag et al, 2005) 27.5770 25.1517 21.0489 Ali et al (1992) 5.880 2.705 2.291 Table II. At different times, L 1 £ 10 3 errors for n ¼ 0:0005 and Dt ¼ 0:01 …”

Section: Numerical Examplesmentioning

confidence: 99%

See 1 more Smart Citation

Numerical solution of the Burgers' equation over geometrically graded mesh

Dağ

Şahin²

2007

Kybernetes

View full text Add to dashboard Cite

KybernetesNumerical solution of the Burgers' equation over geometrically graded mesh İdris Dağ Ali Şahin Article information:To cite this document: İdris Dağ Ali Şahin, (2007),"Numerical solution of the Burgers' equation over geometrically graded mesh", Kybernetes, Vol. 36 Iss 5/6 pp. 721 -735 Permanent link to this document: http://dx.If you would like to write for this, or any other Emerald publication, then please use our Emerald for Authors service information about how to choose which publication to write for and submission guidelines are available for all. Please visit www.emeraldinsight.com/authors for more information. About Emerald www.emeraldinsight.comEmerald is a global publisher linking research and practice to the benefit of society. The company manages a portfolio of more than 290 journals and over 2,350 books and book series volumes, as well as providing an extensive range of online products and additional customer resources and services.Emerald is both COUNTER 4 and TRANSFER compliant. The organization is a partner of the Committee on Publication Ethics (COPE) and also works with Portico and the LOCKSS initiative for digital archive preservation. AbstractPurpose -The purpose of this paper is to illustrate how the numerical solution of the Burgers' equation is obtained using the methods of cubic B-spline collocation and quadratic B-spline Galerkin over the geometrically graded mesh. Design/methodology/approach -The spatial domain is partitioned into geometrically graded mesh. The finite element methods are constructed within the Galerkin and collocation methods using an expansion of the quadratic and cubic B-splines as an approximate function, respectively, over this mesh. Findings -When the higher errors are observed at near boundaries for shock-like and travelling wave solutions of the Burgers' equation, accuracy of the defined methods increase by using finer mesh at near this boundary. Originality/value -Over the geometrically graded mesh definitions of the quadratic B-spline Galerkin and cubic B-spline collocation are given.

show abstract

Section: Numerical Examplesmentioning

confidence: 99%

Section: Numerical Examplesmentioning

confidence: 99%

Numerical solution of the Burgers' equation over geometrically graded mesh

Dağ

Şahin²

2007

Kybernetes

View full text Add to dashboard Cite

show abstract

“…During the past decade, the reasonable increase in the computational power permits many researchers to implement and analyze their numerical schemes to solve Burgers' equation. Few of the most popular methods includes B-spline in conjunction with other methods [32][33][34][35][36], Wavelet-Taylor Galerkin method [37], Adomians decomposition method [38], Haar wavelet quasilinearization method [39], Polynomial based differential quadrature method (QDM) [40,41], Combination of method of lines (MOL) and backward differentiation formula (BDF) [42].…”

Section: Introductionmentioning

confidence: 99%

A differential quadrature based numerical method for highly accurate solutions of Burgers' equation

Aswin

Awasthi

Rashidi

2017

Numerical Methods Partial

View full text Add to dashboard Cite

In this article, we introduce a new, simple, and accurate computational technique for one‐dimensional Burgers' equation. The idea behind this method is the use of polynomial based differential quadrature (PDQ) for the discretization of both time and space derivatives. The quasilinearization process is used for the elimination of nonlinearity. The resultant scheme has simulated for five classic examples of Burgers' equation. The simulation outcomes are validated through comparison with exact and secondary data in the literature for small and large values of kinematic viscosity. The article has deduced that the proposed scheme gives very accurate results even with less number of grid points. The scheme is found to be very simple to implement. Hence, it applies to any domain requires quick implementation and computation.© 2017 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 2023–2042, 2017

show abstract

“…[5] and [6] used the finite difference method. [7] used the direct variational method while [8] used the projection method by B-spline.…”

Section: Introductionmentioning

confidence: 99%

Adomian Decomposition Approach to the Solution of the Burger’s Equation

Akpan¹

2015

AJCM

View full text Add to dashboard Cite

Adomian decomposition method is presented as a method for the solution of the Burger's equation, a popular PDE model in the fluid mechanics. The method is computationally simple in application. The approximate solution is obtained by considering only the first two terms of the decomposition in this paper. Numerical experimentation shows accuracy of a minimum error of order five for various space steps and coefficient of kinematic viscosity. The method is considered high in accuracy.

show abstract

B‐spline collocation methods for numerical solutions of the Burgers′ equation

Cited by 46 publications

References 13 publications

Numerical solution of the Burgers' equation over geometrically graded mesh

Numerical solution of the Burgers' equation over geometrically graded mesh

A differential quadrature based numerical method for highly accurate solutions of Burgers' equation

Adomian Decomposition Approach to the Solution of the Burger’s Equation

Contact Info

Product

Resources

About