Numerical solution of Burgers’ equation with modified cubic B-spline differential quadrature method

Arora, Geeta; Singh, Brajesh Kumar

doi:10.1016/j.amc.2013.08.071

Cited by 99 publications

(73 citation statements)

References 38 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…In [21], Shu and Wu presented an implicit approach using radial basis functions as the test functions. Recently, Arora and Singh [22] used the modified cubic B-spline basis functions, as the test function to solve the non-linear Burgers' equation.…”

Section: Introductionmentioning

confidence: 99%

Numerical solution of some nonlinear wave equations using modified cubic B-spline differential quadrature method

Mittal

Bhatia

2014

2014 International Conference on Advances in Computing, Communications and Informatics (ICACCI)

View full text Add to dashboard Cite

This paper, presents a relatively new approach to solve second order one dimensional non-linear wave equation. We use modified cubic B-spline basis functions based differential quadrature method for space discretization, which gives results in an amenable system of differential equations. The resulting system of equations has been solved using SSP-RK43 scheme. The SSP-RK43 scheme needs less storage space and causes less accumulation of numerical errors. The utility of the scheme is that it does not need any linearization or transformation for handling the non-linear terms and hence reduces the computational effort. The accuracy of the approach has been confirmed with numerical experiments. 2 and ∞ error norms are computed for each example and it is shown that the results obtained are acceptable and are in good agreement with the earlier studies.Keywords-Non-linear wave equations, Modified cubic B-spline basis functions, Differential quadrature method, Thomas algorithm.

show abstract

Section: Introductionmentioning

confidence: 99%

Numerical solution of some nonlinear wave equations using modified cubic B-spline differential quadrature method

Mittal

Bhatia

2014

2014 International Conference on Advances in Computing, Communications and Informatics (ICACCI)

View full text Add to dashboard Cite

show abstract

“…In this paper, we implement MCB-DQM [12,22,23] for numerical computation of Fokker-Planck equations, and Kolmogorov equations. The efficacy of the method has been confirmed by taking three examples having their exact solutions, which shows that MCB-DQM results are acceptable and in good agreement with earlier studies available in literature.…”

Section: Introductionmentioning

confidence: 99%

A Novel Approach for Numerical Computation of Fokker-Planck Equation

Kumar¹,

Singh²,

Nath³

2016

JMSS

View full text Add to dashboard Cite

This paper present an implementation of "modified cubic B-spline differential quadrature method (MCB-DQM)" proposed by Arora & Singh (Applied Mathematics and Computation Vol. 224(1) (2013) 161-177) for numerical computation of Fokker-Planck equations. The modified cubic B-splines are used as set of basis functions in the differential quadrature to compute the weighting coefficients for the spatial derivatives, which reduces Fokker-Planck equation into system of first-order ordinary differential equations (ODEs), in time. The well known SSP-RK43 scheme is then applied to solve the resulting system of ODEs. The efficiency of proposed method has been confirmed by three examples having their exact solutions. This shows that MCB-DQM results are capable of achieving high accuracy. Advantage of the scheme is that it can be applied very smoothly to solve the linear or nonlinear physical problems, and a very less storage space is required which causes less accumulation of numerical errors.

show abstract

“…In this paper, the combination of the trigonometric cubic B-spline(TCB) collocation method and Crank-Nicolson schme(CNS) is applied to integrate FE into a system of nonlinear equations. Some methods endowed with splines are set up to solve the differential equations [17,20,22,23]. There exist spline based numerical methods for the FE in the literature: The FE is solved numerically by setting up an Galerkin method with cubic B-spline over the finite elements in work [2].…”

Section: Introductionmentioning

confidence: 99%

The Numerical Approach to the Fisher's Equation via Trigonometric Cubic B-spline Collocation Method

Hepson¹,

Dağ²

2017

Communications in Numerical Analysis

View full text Add to dashboard Cite

In this study, we set up a numerical technique to get approximate solutions of Fisher's equation which is integrated fully with help of combination of the trigonometric cubic B-spline functions in space and Crank-Nicolson in time. Numerical results have been presented to show utility of the current algorithm by studying three test problems. Solutions of the fisher equation are shown to model the wave front numerically and interaction of diffusion and reaction is observed for the Fisher eqaution.

show abstract

Numerical solution of Burgers’ equation with modified cubic B-spline differential quadrature method

Cited by 99 publications

References 38 publications

Numerical solution of some nonlinear wave equations using modified cubic B-spline differential quadrature method

Numerical solution of some nonlinear wave equations using modified cubic B-spline differential quadrature method

A Novel Approach for Numerical Computation of Fokker-Planck Equation

The Numerical Approach to the Fisher's Equation via Trigonometric Cubic B-spline Collocation Method

Contact Info

Product

Resources

About