A differential quadrature method for numerical solutions of Burgers'‐type equations

Mittal, R. C.; Jiwari, Ram

doi:10.1108/09615531211255761

Cited by 75 publications

(48 citation statements)

References 43 publications

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“…Sinc differential quadrature for the solution of Burgers' equation has been used by Kormaz and Dag [27] . A polynomial Differential quadrature method has been applied by Mittal and Jiwari [28] . Mittal and Bhatia [29] studied hyperbolic telegraph equation by modified B-spline differential quadrature method ( Table 1 ).…”

Section: Introductionmentioning

confidence: 99%

Numerical simulation of reaction-diffusion systems by modified cubic B-spline differential quadrature method

Mittal

Rohila

2016

Chaos, Solitons & Fractals

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Section: Introductionmentioning

confidence: 99%

Numerical simulation of reaction-diffusion systems by modified cubic B-spline differential quadrature method

Mittal

Rohila

2016

Chaos, Solitons & Fractals

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“…We consider Equation (1) Twodimensional Burgers' equations This problem has been considered in Khater et al (2008), Mittal and Jiwari (2012) and Kutluay and Yagmurlu (2012). In our first computation, we take R ¼ 1 and we compute solutions at different time levels for different values of time step Δt and different sizes of the grid.…”

Section: Examplementioning

confidence: 99%

“…Viswanadham and Koneru (1993) redefined the cubic B-spline functions and used them to obtain the numerical solutions of 2D coupled Burgers equations. Mittal and Jiwari (2012) proposed differential quadrature methods to obtain numerical solutions of 2D Burgers equation. A Lattice Boltzmann method has been proposed by Zhang and Yan (2008) while a fourth-order compact finite difference method has been proposed by Liao (2010).…”

Section: Introductionmentioning

confidence: 99%

Numerical solutions of two-dimensional Burgers’ equations using modified Bi-cubic B-spline finite elements

Mittal

Tripathi

2015

Engineering Computations

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Article information:To cite this document: R C Mittal Amit Tripathi , (2015),"Numerical solutions of two-dimensional Burgers' equations using modified Bi-cubic B-spline finite elements", Engineering Computations, Vol. 32 Iss 5 pp. 1275 -1306 Permanent link to this document: http://dx. AbstractPurpose -The purpose of this paper is to develop an efficient numerical scheme for non-linear twodimensional (2D) parabolic partial differential equations using modified bi-cubic B-spline functions. As a test case, method has been applied successfully to 2D Burgers equations. Design/methodology/approach -The scheme is based on collocation of modified bi-cubic B-Spline functions. The authors used these functions for space variable and for its derivatives. Collocation form of the partial differential equation results into system of first-order ordinary differential equations (ODEs). The obtained system of ODEs has been solved by strong stability preserving Runge-Kutta method. The computational complexity of the method is O(p log(p)), where p denotes total number of mesh points. Findings -Obtained numerical solutions are better than those available in literature. Ease of implementation and very small size of computational work are two major advantages of the present method. Moreover, this method provides approximate solutions not only at the grid points but also at any point in the solution domain. Originality/value -First time, modified bi-cubic B-spline functions have been applied to non-linear 2D parabolic partial differential equations. Efficiency of the proposed method has been confirmed with numerical experiments. The authors conclude that the method provides convergent approximations and handles the equations very well in different cases.

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“…Korkmaz and Dag [20,21] have used cosine expansion based differential quadrature method and sinc differential quadrature method for many nonlinear partial differential equations. Mittal et al [22][23][24][25] proposed the polynomial based differential quadrature method for numerical solutions of nonlinear partial differential equations. Here, in this article an approach based on modified cubic B-spline functions has been proposed to find the weighting coefficients of differential quadrature method.…”

Section: Description Of Modified Cubic B-spline Differential Quadratumentioning

confidence: 99%

Numerical simulation on hyperbolic diffusion equations using modified cubic B-spline differential quadrature methods

Mittal

Dahiya

2015

Computers & Mathematics with Applications

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Available online xxxx Keywords:Hyperbolic diffusion problem Cubic B-spline functions Modified cubic B-spline differential quadrature method System of ordinary differential equations Runge-Kutta 4th order method a b s t r a c tIn this article, a modified cubic B-spline differential quadrature method (MCB-DQM) is proposed to solve a hyperbolic diffusion problem in which flow motion is affected by both convection and diffusion. One dimensional hyperbolic non-homogeneous heat, wave and telegraph equations are also considered along with two dimensional hyperbolic diffusion problem. The method reduces the hyperbolic problem into a system of nonlinear ordinary differential equations. The system is then solved by the optimal four stage three order strong stability-preserving time stepping Runge-Kutta (SSP-RK43) scheme. The reliability and efficiency of the method has been tested on seven examples. The stability of the method is also discussed and found to be unconditionally stable.

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A differential quadrature method for numerical solutions of Burgers'‐type equations

Cited by 75 publications

References 43 publications

Numerical simulation of reaction-diffusion systems by modified cubic B-spline differential quadrature method

Numerical simulation of reaction-diffusion systems by modified cubic B-spline differential quadrature method

Numerical solutions of two-dimensional Burgers’ equations using modified Bi-cubic B-spline finite elements

Numerical simulation on hyperbolic diffusion equations using modified cubic B-spline differential quadrature methods

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