Related papers: An improved Haar wavelet quasilinearization techni…
This paper presents a numerical method to solve a time-fractional Burgers equation, achieving order of convergence $(2-\alpha)$ in time, here $\alpha$ represents the order of the time derivative. The fractional derivative is modeled by…
We provide a detailed numerical study of various issues pertaining to the dynamics of the Burgers equation perturbed by a weak dispersive term: blow-up in finite time versus global existence, nature of the blow-up, existence for "long"…
We study a formulation of Burgers equation on the Sierpinski gasket, which is the prototype of a p.c.f. self-similar fractal. One possibility is to implement Burgers equation as a semilinear heat equation associated with the Laplacian for…
A hierarchy of normalized classes of generalized Burgers equations is studied. The equivalence groupoids of these classes are computed. The equivalence groupoids of classes of linearizable generalized Burgers equations are related to those…
In this paper we study the asymptotic behaviour of solutions of a system of $N$ partial differential equations. When $N = 1$ the equation reduces to the Burgers equation and was studied by Hopf. We consider both the inviscid and viscous…
In this paper, semi-discrete numerical scheme for the approximation of the periodic Vlasov-viscous Burgers' system is developed and analyzed. The scheme is based on the coupling of discontinuous Galerkin approximations for the Vlasov…
In this study, a thorough investigation was conducted into the Homotopy Perturbation Method (HPM) and its application to solve the Burger and Blasius equations. The HPM is a mathematical technique that combines aspects of homotopy and…
In this paper, we analyze the three-level explicit time-split MacCormack procedure in the numerical solutions of two-dimensional viscous coupled Burgers' equations subject to initial and boundary conditions. The differential operators split…
We study the traveling wave solutions of the Burgers-Huxley equation from a geometric point of view via the qualitative theory of ordinary differential equations. By using the Poincar\'e compactification we study the global phase portraits…
This work aims to construct an efficient and highly accurate numerical method to address the time singularity at $t=0$ involved in a class of time-fractional parabolic integro-partial differential equations in one and two dimensions. The…
We study the small dispersion limit of the intermediate long wave (ILW) equation, specifically on a class of well-behaved initial conditions $u_0$ where the number of solitons in the solution increases without bound. First, we conduct a…
A Lax pair consisting of the Forsyth-Hopf-Cole transformation and a linear differential (in time) - difference (in continuous space) equation generates the whole hierarchy of the Burgers equation and admits exact moving front solutions.…
In this paper we study the approximation of the distribution of $X_t$ Hilbert--valued stochastic process solution of a linear parabolic stochastic partial differential equation written in an abstract form as $$ dX_t+AX_t dt = Q^{1/2} d W_t,…
Using the fractional derivative, considered in the Caputo sense, we study an analytical technique associated with the variational iteration method for the fractional generalized $\alpha$-time Burgers' equation with $\alpha>0$ and obtain…
We propose a novel efficient and robust Wavelet-based Edge Multiscale Finite Element Method (WEMsFEM) motivated by \cite{MR3980476,GL18} to solve the singularly perturbed convection-diffusion equations. The main idea is to first establish a…
We propose a model reduction procedure for rapid and reliable solution of parameterized hyperbolic partial differential equations. Due to the presence of parameter-dependent shock waves and contact discontinuities, these problems are…
In this article, we present the time-space Chebyshev pseudospectral method (TS-CPsM) to approximate a solution to the generalised Burgers-Fisher (gBF) equation. The Chebyshev-Gauss-Lobatto (CGL) points serve as the foundation for the…
We consider an initial value problem for a quadratically nonlinear inviscid Burgers-Hilbert equation that models the motion of vorticity discontinuities. We use a modified energy method to prove the existence of small, smooth solutions over…
This paper addresses the problem of finding a B-term wavelet representation of a given discrete function $f \in \real^n$ whose distance from f is minimized. The problem is well understood when we seek to minimize the Euclidean distance…
In the first part of this paper, we prove the global regularity, in an adequate parabolic Bessel-Potential space and then in the corresponding parabolic fractional Sobolev space, of the unique solution to following fractional heat equation…