A First Step in Applying the Sinc Collocation Method to the Nonlinear Navier-Stokes Equations

Narasimhan, Susheela; Majdalani, Joseph; Stenger, Frank

doi:10.1080/104077902753725902

Cited by 21 publications

(4 citation statements)

References 22 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The LSF, on the other hand, apply directly to a finite domain. We can test the performance of the LSF on an example selected from [14]:…”

Section: Little Sinc Functionsmentioning

confidence: 99%

“…Collocation methods based on ordinary sinc function have been applied in the literature to a large class of problems, which include those mentioned above (see, for example, [9]), and they have been put on firm mathematical grounds [10]. Examples of applications of the sinc functions can be found in [11][12][13][14][15][16], among others. Recently, one of the authors has shown that the sinc collocation methods can be optimized by using a variational approach [17] based on the principle of minimal sensitivity (PMS) [18].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Variational collocation on finite intervals

Amore¹,

Cervantes²,

Fernández³

2007

J. Phys. A: Math. Theor.

View full text Add to dashboard Cite

In this paper we study a new family of sinc-like functions, defined on an interval of finite width. These functions, which we call "little sinc", are orthogonal and share many of the properties of the sinc functions. We show that the little sinc functions supplemented with a variational approach enable one to obtain accurate results for a variety of problems. We apply them to the interpolation of functions on finite domain and to the solution of the Schrödinger equation, and compare the performance of present approach with others.

show abstract

“…The LSF, on the other hand, apply directly to a finite domain. We can test the performance of the LSF on an example selected from [14]:…”

Section: Little Sinc Functionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Variational collocation on finite intervals

Amore¹,

Cervantes²,

Fernández³

2007

J. Phys. A: Math. Theor.

View full text Add to dashboard Cite

show abstract

“…In the work of Stenger [23], some problems related to medical problems are taken and numerical results are found using Sinc methods. In [24], a new algorithm based on Sinc method is applied for the solution of a nonlinear set of PDEs. A new SGM is illustrated for the numerical solutions of convection diffusion equations on half-infinite intervals in [25].…”

Section: Introductionmentioning

confidence: 99%

Sinc-Galerkin method for solving hyperbolic partial differential equations

Seçer

2018

Int. J. Optim. Control, Theor. Appl. (IJOCTA)

View full text Add to dashboard Cite

In this work, we consider the hyperbolic equations to determine the approximate solutions via Sinc-Galerkin Method (SGM). Without any numerical integration, the partial differential equation transformed to an algebraic equation system. For the numerical calculations, Maple is used. Several numerical examples are investigated and the results determined from the method are compared with the exact solutions. The results are illustrated both in the table and graphically.

show abstract

“…The DE formula has been widely used in the last three decades and is now recognized to be one of the most efficient quadrature formulae [13,14]. The use of the DE transformation technique in the Sinc method yields a highly efficient numerical method for interpolation, quadrature, approximation of transformation, differential and partial differential equations [14][15][16].…”

Section: Introductionmentioning

confidence: 99%

A Sinc‐collocation method with boundary treatment for the Stokes equations

2006

Numerical Methods in Fluids

View full text Add to dashboard Cite

SUMMARYIn Stokes equations the velocity u and the pressure p are coupled together by the imcompressibility condition div u = 0 which makes the equations difficult to solve numerically. In this paper, a method named Sinc-collocation method with boundary treatment (SCMBT) is applied to the Stokes equations. The numerical results show that our method is of high accuracy, of good convergence with little computational effort.

show abstract

A First Step in Applying the Sinc Collocation Method to the Nonlinear Navier-Stokes Equations

Cited by 21 publications

References 22 publications

Variational collocation on finite intervals

Variational collocation on finite intervals

Sinc-Galerkin method for solving hyperbolic partial differential equations

A Sinc‐collocation method with boundary treatment for the Stokes equations

Contact Info

Product

Resources

About