Mathematical Methods in the Applied Sciences, ISSN 0170-4214, 03/2017, Volume 40, Issue 5, pp. 1598 - 1607

Propagation of two‐dimensional nonlinear ion‐acoustic solitary waves and shocks in a dissipative quantum plasma is analyzed. By applying the reductive...

mathematical methods | Kadomtsev–Petviashvili–Burgers equation | quantum plasma | ion acoustic solitary waves | MATHEMATICS, APPLIED | SCHRODINGER-EQUATION | ZAKHAROV-KUZNETSOV EQUATION | INSTABILITIES | Kadomtsev-Petviashvili-Burgers equation | VARIATIONAL METHOD | MAGNETOHYDRODYNAMIC FLOWS | STABILITY ANALYSIS | DISPERSIVE WAVES | DUSTY PLASMA | Algebra | Wave propagation | Two-dimensional analysis | Mathematical analysis | Dissipation | Nonlinearity | Mathematical models | Solitary waves

mathematical methods | Kadomtsev–Petviashvili–Burgers equation | quantum plasma | ion acoustic solitary waves | MATHEMATICS, APPLIED | SCHRODINGER-EQUATION | ZAKHAROV-KUZNETSOV EQUATION | INSTABILITIES | Kadomtsev-Petviashvili-Burgers equation | VARIATIONAL METHOD | MAGNETOHYDRODYNAMIC FLOWS | STABILITY ANALYSIS | DISPERSIVE WAVES | DUSTY PLASMA | Algebra | Wave propagation | Two-dimensional analysis | Mathematical analysis | Dissipation | Nonlinearity | Mathematical models | Solitary waves

Journal Article

Computers and Mathematics with Applications, ISSN 0898-1221, 02/2018, Volume 75, Issue 3, pp. 864 - 875

In this paper, two lattice Boltzmann models for two-dimensional coupled Burgers’ equations are proposed through treating the part or all of convection items as...

Two-dimensional coupled Burgers’ equations | Lattice Boltzmann model | Source term | CONVECTION-DIFFUSION EQUATIONS | SCHEME | MATHEMATICS, APPLIED | Two-dimensional coupled Burgers' equations | FLOWS

Two-dimensional coupled Burgers’ equations | Lattice Boltzmann model | Source term | CONVECTION-DIFFUSION EQUATIONS | SCHEME | MATHEMATICS, APPLIED | Two-dimensional coupled Burgers' equations | FLOWS

Journal Article

Computers and Mathematics with Applications, ISSN 0898-1221, 01/2019, Volume 77, Issue 2, pp. 565 - 575

This work addresses, numerical method based on Haar wavelets and finite differences to solve two dimensional linear, nonlinear Sobolev and non-linear...

Finite differences | Two dimensional Haar wavelets | Non-linear PDEs | MATHEMATICS, APPLIED | FINITE-ELEMENT-METHOD | ALGORITHM | Wavelet | Norms | Collocation methods | Computation | Numerical methods

Finite differences | Two dimensional Haar wavelets | Non-linear PDEs | MATHEMATICS, APPLIED | FINITE-ELEMENT-METHOD | ALGORITHM | Wavelet | Norms | Collocation methods | Computation | Numerical methods

Journal Article

Physica A: Statistical Mechanics and its Applications, ISSN 0378-4371, 2006, Volume 361, Issue 2, pp. 394 - 404

By means of the modified extended tanh-function (METF) method the multiple travelling wave solutions of some different kinds of nonlinear partial differential...

The METF method | Burgers’ equation | Two-dimensional Burgers’ equations | Coupled Burgers’ equations | KdV–Burgers’ equation | KdV-Burgers' equation | Burgers' equation | Two-dimensional Burgers' equations | Coupled Burgers' equations | TRANSFORMATION | coupled burgers' equations | PHYSICS, MULTIDISCIPLINARY | DECOMPOSITION METHOD | COUPLED KDV EQUATION | two-dimensional Burgers' equations | KORTEWEG-DEVRIES EQUATION | PARTIAL-DIFFERENTIAL EQUATIONS | SOLITARY WAVE SOLUTIONS | the METF method | NONLINEAR EVOLUTION-EQUATIONS

The METF method | Burgers’ equation | Two-dimensional Burgers’ equations | Coupled Burgers’ equations | KdV–Burgers’ equation | KdV-Burgers' equation | Burgers' equation | Two-dimensional Burgers' equations | Coupled Burgers' equations | TRANSFORMATION | coupled burgers' equations | PHYSICS, MULTIDISCIPLINARY | DECOMPOSITION METHOD | COUPLED KDV EQUATION | two-dimensional Burgers' equations | KORTEWEG-DEVRIES EQUATION | PARTIAL-DIFFERENTIAL EQUATIONS | SOLITARY WAVE SOLUTIONS | the METF method | NONLINEAR EVOLUTION-EQUATIONS

Journal Article

Applied Mathematics and Computation, ISSN 0096-3003, 09/2014, Volume 243, pp. 960 - 962

In a paper by Liu and Hou (2011) [1] the fractional coupled Burgers equation is solved by generalized two dimensional differential transform method. Two...

Two dimensional differential transform | Generalized differential transform method | Fractional coupled Burgers equation | MATHEMATICS, APPLIED

Two dimensional differential transform | Generalized differential transform method | Fractional coupled Burgers equation | MATHEMATICS, APPLIED

Journal Article

Personal and Ubiquitous Computing, ISSN 1617-4909, 10/2018, Volume 22, Issue 5, pp. 1133 - 1139

The Burgers’ equation as a useful mathematical model is applied in many fields such as fluid dynamic, heat conduction, and continuous stochastic processes....

Computer Science | User Interfaces and Human Computer Interaction | Optimal error estimate | Burgers’ equation | Finite volume method | Computer Science, general | Mobile Computing | Personal Computing | SPACE | NUMERICAL-SOLUTION | ELEMENT METHODS | COMPUTER SCIENCE, INFORMATION SYSTEMS | Burgers' equation | TIME | TELECOMMUNICATIONS | Fluid dynamics | Analysis | Stochastic processes | Methods | Finite element method | Conductive heat transfer | Numerical methods | Conduction heating | Two dimensional models | Mathematical models | Heat transfer

Computer Science | User Interfaces and Human Computer Interaction | Optimal error estimate | Burgers’ equation | Finite volume method | Computer Science, general | Mobile Computing | Personal Computing | SPACE | NUMERICAL-SOLUTION | ELEMENT METHODS | COMPUTER SCIENCE, INFORMATION SYSTEMS | Burgers' equation | TIME | TELECOMMUNICATIONS | Fluid dynamics | Analysis | Stochastic processes | Methods | Finite element method | Conductive heat transfer | Numerical methods | Conduction heating | Two dimensional models | Mathematical models | Heat transfer

Journal Article

Journal of Computational Physics, ISSN 0021-9991, 2010, Volume 229, Issue 19, pp. 7147 - 7161

A new numerical method, which is based on the coupling between variational multiscale method and meshfree methods, is developed for 2D Burgers’ equation with...

Variational multiscale | Burgers’ equation | Meshfree method | Burgers' equation | NUMERICAL-SOLUTION | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | FINITE-ELEMENT | PARTITION | PHYSICS, MATHEMATICAL | BUBBLES | Finite element method | Computation | Mathematical analysis | Meshless methods | Mathematical models | Two dimensional | Galerkin methods | Mesh generation

Variational multiscale | Burgers’ equation | Meshfree method | Burgers' equation | NUMERICAL-SOLUTION | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | FINITE-ELEMENT | PARTITION | PHYSICS, MATHEMATICAL | BUBBLES | Finite element method | Computation | Mathematical analysis | Meshless methods | Mathematical models | Two dimensional | Galerkin methods | Mesh generation

Journal Article

Computers & Mathematics with Applications, ISSN 0898-1221, 02/2018, Volume 75, Issue 3, p. 864

In this paper, two lattice Boltzmann models for two-dimensional coupled Burgers’ equations are proposed through treating the part or all of convection items as...

Studies | Two dimensional models | Mathematical models | Linear equations | Convection | Distribution functions

Studies | Two dimensional models | Mathematical models | Linear equations | Convection | Distribution functions

Journal Article

International Journal of Numerical Methods for Heat & Fluid Flow, ISSN 0961-5539, 09/2012, Volume 22, Issue 7, pp. 880 - 895

Purpose - The purpose of this paper is to use the polynomial differential quadrature method (PDQM) to find the numerical solutions of some Burgers'-type...

1D Burgers' equation | 2D Burgers' equation | Differential equations | Mathematics | Runge-Kutta method | Coupled Burgers' equations | Differential quadrature method | ALGORITHM | SCHEME | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | THERMODYNAMICS | FINITE-ELEMENT | EXPLICIT | Studies | Problems | Algorithms | Partial differential equations | Ordinary differential equations | Boundary conditions | Physics | Methods | Mathematical analysis | Nonlinear differential equations | Nonlinearity | Mathematical models | Two dimensional

1D Burgers' equation | 2D Burgers' equation | Differential equations | Mathematics | Runge-Kutta method | Coupled Burgers' equations | Differential quadrature method | ALGORITHM | SCHEME | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | THERMODYNAMICS | FINITE-ELEMENT | EXPLICIT | Studies | Problems | Algorithms | Partial differential equations | Ordinary differential equations | Boundary conditions | Physics | Methods | Mathematical analysis | Nonlinear differential equations | Nonlinearity | Mathematical models | Two dimensional

Journal Article

Computers and Mathematics with Applications, ISSN 0898-1221, 2010, Volume 60, Issue 3, pp. 840 - 848

In this paper, the discrete Adomian decomposition method (ADM) is proposed to numerically solve the two-dimensional Burgers’ nonlinear difference equations....

Finite difference scheme | Discrete Adomian decomposition method | Numerical solutions | Burgers’ equations | Two-dimensional | Burgers' equations | TRANSFORMATION | MATHEMATICS, APPLIED | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | FINITE-DIFFERENCE SCHEME | Accuracy | Computer simulation | Difference equations | Mathematical analysis | Exact solutions | Nonlinearity | Decomposition | Mathematical models | Two dimensional

Finite difference scheme | Discrete Adomian decomposition method | Numerical solutions | Burgers’ equations | Two-dimensional | Burgers' equations | TRANSFORMATION | MATHEMATICS, APPLIED | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | FINITE-DIFFERENCE SCHEME | Accuracy | Computer simulation | Difference equations | Mathematical analysis | Exact solutions | Nonlinearity | Decomposition | Mathematical models | Two dimensional

Journal Article

Applied Mathematics and Computation, ISSN 0096-3003, 2011, Volume 217, Issue 16, pp. 7001 - 7008

In this paper, by introducing the fractional derivative in the sense of Caputo, the generalized two-dimensional differential transform method (DTM) is directly...

Generalized Taylor series formula | Fractional coupled Burgers equations | Caputo fractional derivative | Numerical solutions | Differential transform method | MATHEMATICS, APPLIED | ALGORITHM | Numerical analysis | Mathematical analysis | Transforms | Differential equations | Taylor series | Mathematical models | Derivatives | Burgers equation | Two dimensional

Generalized Taylor series formula | Fractional coupled Burgers equations | Caputo fractional derivative | Numerical solutions | Differential transform method | MATHEMATICS, APPLIED | ALGORITHM | Numerical analysis | Mathematical analysis | Transforms | Differential equations | Taylor series | Mathematical models | Derivatives | Burgers equation | Two dimensional

Journal Article

ROMANIAN JOURNAL OF PHYSICS, ISSN 1221-146X, 2017, Volume 62, Issue 1-2

The purpose of this study is to investigate a combination between the homotopy analysis method and finite differences for the numerical resolution of coupled...

coupled two dimensional Burgers' equation | nonlinear partial differential equations | FLUID | PHYSICS, MULTIDISCIPLINARY | homotopy analysis method | ANALYTIC SOLUTION | NONLINEAR POISSON EQUATION | VISCOUS-FLOW | DIFFERENTIAL-EQUATIONS | APPROXIMATE SOLUTION | BOUNDARY-ELEMENT METHOD | finite differences method

coupled two dimensional Burgers' equation | nonlinear partial differential equations | FLUID | PHYSICS, MULTIDISCIPLINARY | homotopy analysis method | ANALYTIC SOLUTION | NONLINEAR POISSON EQUATION | VISCOUS-FLOW | DIFFERENTIAL-EQUATIONS | APPROXIMATE SOLUTION | BOUNDARY-ELEMENT METHOD | finite differences method

Journal Article

Applied Mathematics and Computation, ISSN 0096-3003, 08/2016, Volume 286, pp. 1 - 14

The numerical solution of the initial value problem for the two-dimensional Burgers equation on the whole plane is considered. Usual techniques, like finite...

Finite element method | Fourier transform | Burgers equation | Boundless domain | SYSTEM | MATHEMATICS, APPLIED | DECOMPOSITION METHOD | TIME | FINITE-DIFFERENCE SCHEME | FLOW | NUMERICAL-SOLUTION | WAVES | DISCRETIZATION | ELEMENT | TURBULENCE | Planes | Mathematical analysis | Boundary conditions | Initial value problems | Mathematical models | Two dimensional | Finite difference method

Finite element method | Fourier transform | Burgers equation | Boundless domain | SYSTEM | MATHEMATICS, APPLIED | DECOMPOSITION METHOD | TIME | FINITE-DIFFERENCE SCHEME | FLOW | NUMERICAL-SOLUTION | WAVES | DISCRETIZATION | ELEMENT | TURBULENCE | Planes | Mathematical analysis | Boundary conditions | Initial value problems | Mathematical models | Two dimensional | Finite difference method

Journal Article

Communications in Nonlinear Science and Numerical Simulation, ISSN 1007-5704, 10/2016, Volume 39, pp. 283 - 299

•We use Lie symmetry method to perform an exhaustive analysis on the system of 2D Burgers equations.•Optimal system of one-dimensional subalgebras were...

2D fluid turbulence | Conservation laws | 2D Burgers equations | Exact solutions | MATHEMATICS, APPLIED | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | PHYSICS, FLUIDS & PLASMAS | SOLVING BURGERS | TURBULENCE | PHYSICS, MATHEMATICAL | Laws, regulations and rules | Turbulence | Environmental law | Algorithms | Fluid dynamics | Turbulent flow | Computational fluid dynamics | Mathematical analysis | Fluid flow | Mathematical models | Burgers equation | Two dimensional

2D fluid turbulence | Conservation laws | 2D Burgers equations | Exact solutions | MATHEMATICS, APPLIED | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | PHYSICS, FLUIDS & PLASMAS | SOLVING BURGERS | TURBULENCE | PHYSICS, MATHEMATICAL | Laws, regulations and rules | Turbulence | Environmental law | Algorithms | Fluid dynamics | Turbulent flow | Computational fluid dynamics | Mathematical analysis | Fluid flow | Mathematical models | Burgers equation | Two dimensional

Journal Article

National Academy Science Letters, ISSN 0250-541X, 10/2018, Volume 41, Issue 5, pp. 295 - 299

The analytical solution of nonlinear two dimensional space–time fractional Burgers–Huxley equation involving Jumarie’s modified Riemann–Liouville derivative is...

History of Science | Fractional Ricatti equation | Fractional order derivative | Burgers–Huxley equation | Fractional sub-equation method | Science, Humanities and Social Sciences, multidisciplinary | ORDER | TRAVELING-WAVE SOLUTIONS | COLLOCATION METHOD | Burgers-Huxley equation | MULTIDISCIPLINARY SCIENCES | DIFFERENTIAL-EQUATIONS | EVOLUTION-EQUATIONS | FISHER EQUATIONS

History of Science | Fractional Ricatti equation | Fractional order derivative | Burgers–Huxley equation | Fractional sub-equation method | Science, Humanities and Social Sciences, multidisciplinary | ORDER | TRAVELING-WAVE SOLUTIONS | COLLOCATION METHOD | Burgers-Huxley equation | MULTIDISCIPLINARY SCIENCES | DIFFERENTIAL-EQUATIONS | EVOLUTION-EQUATIONS | FISHER EQUATIONS

Journal Article

Engineering Analysis with Boundary Elements, ISSN 0955-7997, 2008, Volume 32, Issue 5, pp. 395 - 412

The Eulerian–Lagrangian method of fundamental solutions is proposed to solve the two-dimensional unsteady Burgers’ equations. Through the Eulerian–Lagrangian...

Diffusion fundamental solution | Eulerian–Lagrangian method | Method of fundamental solutions | Meshless method | Burgers’ equations | Eulerian-Lagrangian method | Burgers' equations | meshless method | SCHEME | diffusion fundamental solution | NUMERICAL-SOLUTION | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | ENGINEERING, MULTIDISCIPLINARY | GALERKIN MLPG METHOD | method of fundamental solutions | DIFFUSION-PROBLEMS | FINITE-ELEMENT | Finite element method | Mathematical analysis | Meshless methods | Disturbances | Mathematical models | Unsteady | Two dimensional | Diffusion

Diffusion fundamental solution | Eulerian–Lagrangian method | Method of fundamental solutions | Meshless method | Burgers’ equations | Eulerian-Lagrangian method | Burgers' equations | meshless method | SCHEME | diffusion fundamental solution | NUMERICAL-SOLUTION | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | ENGINEERING, MULTIDISCIPLINARY | GALERKIN MLPG METHOD | method of fundamental solutions | DIFFUSION-PROBLEMS | FINITE-ELEMENT | Finite element method | Mathematical analysis | Meshless methods | Disturbances | Mathematical models | Unsteady | Two dimensional | Diffusion

Journal Article

Nonlinear Analysis: Real World Applications, ISSN 1468-1218, 06/2015, Volume 23, pp. 123 - 128

In this work we study the Kadomtsev–Petviashvili–Burgers equation, which is a natural model for the propagation of the two-dimensional damped waves. We show...

Lie point symmetry | Conservation law | Nonlinear self-adjointness | Ibragimov’s theorem | Ibragimov's theorem | MATHEMATICS, APPLIED | Environmental law | Analysis | Conservation laws | Theorems | Wave propagation | Equivalence | Mathematical analysis | Nonlinearity | Mathematical models | Two dimensional

Lie point symmetry | Conservation law | Nonlinear self-adjointness | Ibragimov’s theorem | Ibragimov's theorem | MATHEMATICS, APPLIED | Environmental law | Analysis | Conservation laws | Theorems | Wave propagation | Equivalence | Mathematical analysis | Nonlinearity | Mathematical models | Two dimensional

Journal Article

Engineering Computations, ISSN 0264-4401, 07/2015, Volume 32, Issue 5, pp. 1275 - 1306

Purpose – The purpose of this paper is to develop an efficient numerical scheme for non-linear two-dimensional (2D) parabolic partial differential equations...

Engineering | Aerospace engineering | Hockney method | Two-dimensional coupled Burgers' equations | Collocation method | Two-dimensional Burgers' equation | Modified bi-cubic B-splines | SSP-RK54 scheme | SYSTEM | DECOMPOSITION METHOD | DIFFERENTIAL QUADRATURE METHOD | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | ENGINEERING, MULTIDISCIPLINARY | SCALING FUNCTIONS | SCHEMES | Viscosity | B spline functions | Partial differential equations | Collocation | Computation | Test procedures | Design modifications | Reynolds number | Ordinary differential equations | Boundary conditions | Runge-Kutta method | Methods

Engineering | Aerospace engineering | Hockney method | Two-dimensional coupled Burgers' equations | Collocation method | Two-dimensional Burgers' equation | Modified bi-cubic B-splines | SSP-RK54 scheme | SYSTEM | DECOMPOSITION METHOD | DIFFERENTIAL QUADRATURE METHOD | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | ENGINEERING, MULTIDISCIPLINARY | SCALING FUNCTIONS | SCHEMES | Viscosity | B spline functions | Partial differential equations | Collocation | Computation | Test procedures | Design modifications | Reynolds number | Ordinary differential equations | Boundary conditions | Runge-Kutta method | Methods

Journal Article

Applied Mathematics and Computation, ISSN 0096-3003, 05/2015, Volume 258, pp. 296 - 311

The generalized Burger's-Huxley and Burger's-Fisher equations are solved by fully different numerical scheme. The equations are discretized in time by a new...

2N order compact finite difference scheme | Generalized Burger's-Fisher equation | Two-dimensional unsteady Burger's equation | Collocation method | Generalized Burger's-Huxley equation | MATHEMATICS, APPLIED

2N order compact finite difference scheme | Generalized Burger's-Fisher equation | Two-dimensional unsteady Burger's equation | Collocation method | Generalized Burger's-Huxley equation | MATHEMATICS, APPLIED

Journal Article

Applied Mathematics and Computation, ISSN 0096-3003, 2011, Volume 217, Issue 15, pp. 6671 - 6679

The two-dimensional Burgers’ equations are solved here using the A Priori Reduction method. This method is based on an iterative procedure which consists in...

Proper orthogonal decomposition (POD) | Karhunen–Loéve decomposition | Reduced-order model | Burgers’ equations | Karhunen-Loéve decomposition | Burgers' equations | MATHEMATICS, APPLIED | MODEL-REDUCTION | TURBULENCE | Karhunen-Loeve decomposition | Reduction | Computation | Mathematical analysis | Newton Raphson methods | Decomposition | Mathematical models | Iterative methods | Two dimensional | Standards | Engineering Sciences | Materials

Proper orthogonal decomposition (POD) | Karhunen–Loéve decomposition | Reduced-order model | Burgers’ equations | Karhunen-Loéve decomposition | Burgers' equations | MATHEMATICS, APPLIED | MODEL-REDUCTION | TURBULENCE | Karhunen-Loeve decomposition | Reduction | Computation | Mathematical analysis | Newton Raphson methods | Decomposition | Mathematical models | Iterative methods | Two dimensional | Standards | Engineering Sciences | Materials

Journal Article

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