Burgers equation with time-dependent coefficients and nonlinear forcing term: Linearization and exact solvability

Schulze-Halberg, Axel

doi:10.1016/j.cnsns.2014.08.029

Cited by 8 publications

(6 citation statements)

References 21 publications

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“…. , solution of the heat problem again can be written as in (27) and the corresponding solution of the Burgers problem (57) becomes…”

Section: Modelmentioning

confidence: 99%

“…In [26] we investigated the pure IVP with initial condition U (x, t 0 ) = F (x ) on the whole line −∞ < x < ∞ . Linearization and exact solvability of a generalization of this problem was given by Schulze-Halberg in [27] , and very recently in [28] authors solved the Cauchy problem for Burgers hierarchy and forced Burgers equation with general time-dependent coefficients, using the Green's function of the corresponding linear problem.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Dirichlet problem on the half-line for a forced Burgers equation with time-variable coefficients and exactly solvable models

Büyükaşık

Bozacı

2020

Communications in Nonlinear Science and Numerical Simulation

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“…. , solution of the heat problem again can be written as in (27) and the corresponding solution of the Burgers problem (57) becomes…”

Section: Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Dirichlet problem on the half-line for a forced Burgers equation with time-variable coefficients and exactly solvable models

Büyükaşık

Bozacı

2020

Communications in Nonlinear Science and Numerical Simulation

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“…Recently Büyükaşik and Pashaev [33] and Schulze-Halberg [34] detailed a linearising transform of the Burgers equation with general forcing term and time dependent coefficients. Using results from these aforementioned studies, we focus on generating solutions to the Cauchy problem of the two following systems: 1) the Burgers hierarchy with general time dependent coefficients,…”

Section: Focus Of This Work: Hierarchy and Forced Burgers With Time D...mentioning

confidence: 99%

“…Additionally, although Eq. ( 5) was first posed in [34] and solved for various potentials and initial conditions, in this work we derive the Green's function for the corresponding linearised system.…”

Section: Focus Of This Work: Hierarchy and Forced Burgers With Time D...mentioning

confidence: 99%

Green’s functions and the Cauchy problem of the Burgers hierarchy and forced Burgers equation

Zuparic

Hoek

2019

Communications in Nonlinear Science and Numerical Simulation

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We consider the Cauchy problem for the Burgers hierarchy with general time dependent coefficients. The closed form for the Green's function of the corresponding linear equation of arbitrary order N is shown to be a sum of generalised hypergeometric functions. For suitably damped initial conditions we plot the time dependence of the Cauchy problem over a range of N values. For N = 1, we introduce a spatial forcing term. Using connections between the associated second order linear Schrödinger and Fokker-Planck equations, we give closed form expressions for the corresponding Green's functions of the sinked Bessel process with constant drift. We then apply the Green's function to give time dependent profiles for the corresponding forced Burgers Cauchy problem.

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“…Hon and Mao in [18] applied the multiquadric (MQ) as a spatial approximation scheme. Schulze-Halberg discussed a linearization method for solving Burgers equation with time dependent coefficients and a non-linear forcing term [19]. In [20], Seydaoglu presented the high-order splitting methods.…”

Section: Introductionmentioning

confidence: 99%

Space–Time Spectral Collocation Method for Solving Burgers Equations with the Convergence Analysis

Skandari

Mohammadizadeh

et al. 2019

Symmetry

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This article deals with a numerical approach based on the symmetric space-time Chebyshev spectral collocation method for solving different types of Burgers equations with Dirichlet boundary conditions. In this method, the variables of the equation are first approximated by interpolating polynomials and then discretized at the Chebyshev–Gauss–Lobatto points. Thus, we get a system of algebraic equations whose solution is the set of unknown coefficients of the approximate solution of the main problem. We investigate the convergence of the suggested numerical scheme and compare the proposed method with several recent approaches through examining some test problems.

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Burgers equation with time-dependent coefficients and nonlinear forcing term: Linearization and exact solvability

Cited by 8 publications

References 21 publications

Dirichlet problem on the half-line for a forced Burgers equation with time-variable coefficients and exactly solvable models

Dirichlet problem on the half-line for a forced Burgers equation with time-variable coefficients and exactly solvable models

Green’s functions and the Cauchy problem of the Burgers hierarchy and forced Burgers equation

Space–Time Spectral Collocation Method for Solving Burgers Equations with the Convergence Analysis

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