Related papers: A New Approach in Solving Regular and Singular Con…
In this paper, the fractional-order Burgers-Poisson equation is introduced by replacing the first-order time derivative by fractional derivative of order $\alpha$. Both exact and approximate explicit solutions are obtained by employing…
This paper modifies a n-dimensional Hopf-Cole transformation to the n-dimensional Burgers' system. We obtain the n-dimensional heat conduction equation through the modification of the Hopf-Cole transformation. Then the fourth-order precise…
We consider the fractional Burgers' equation on $\R^N$ with the critical dissipation term. We follow the parabolic De-Giorgi's method of Caffarelli and Vasseur \cite{Driftdiffusion} and show existence of smooth solutions given any initial…
We propose a conjugated filter oscillation reduction scheme for solving Burgers' equation with high Reynolds numbers. Computational accuracy is tested at a moderately high Reynolds number for which analytical solution is available.…
In terms of Dirac matrices the self-dual and anti-self-dual decomposition of a conformal supergravity is given and a self-dual conformal supergravity theory is developed as a connection dynamic theory in which the basic dynamic variabes…
We explore a computational approach to coarse graining the evolution of the large-scale features of a randomly forced Burgers equation in one spatial dimension. The long term evolution of the solution energy spectrum appears self-similar in…
We study the discretization, convergence, and numerical implementation of recent reformulations of the quadratic porous medium equation (multidimensional and anisotropic) and Burgers' equation (one-dimensional, with optional viscosity), as…
Although being powerful, the differential transform method yet suffers from a drawback which is how to compute the differential transform of nonlinear non-autonomous functions that can limit its applicability. In order to overcome this…
Here we study theoretically and compare experimentally an efficient method for solving systems of algebraic equations, where the matrix comes from the discretization of a fractional diffusion operator. More specifically, we focus on…
This study is motivated by the recent development in the fractional calculus and its applications. During last few years, several different techniques are proposed to localize the nonlocal fractional diffusion operator. They are based on…
The following document presents some novel numerical methods valid for one and several variables, which using the fractional derivative, allow to find solutions for some non-linear systems in the complex space using real initial conditions.…
A special initial condition for (1+1)-dimensional Burgers equation is considered. It allows to obtain new analytical solutions for an arbitrary low viscosity as well as for the inviscid case. The viscous solution is written as a rational…
We generalize the notions of the St\"ackel transform and the coupling constant metamorphosis to quasi-exactly solvable systems. We discover that for a variety of one-dimensional and separable multidimensional quasi-exactly solvable systems,…
The application of the approximation-operational approach to solving linear differential equations of fractional order with variable coefficients is considered. It is shown that the method can also be applied to solving differential…
Two main algorithmic approaches are known for making Hironaka's proof of resolution of singularities in characteristic zero constructive. Their main difference is the use of different notions of transforms during the resolution process and…
We solve the rotational abrasion model of Roth, Marques and Durian (arXiv:1009.3492), a one-dimensional quasilinear partial differential equation resembling the inviscid Burgers equation with the unusual feature of a step function factor as…
Using modified Riemann-Liouville derivative, the Exp function and Exponential rational function methods are implemented to solve the time-fractional generalized Burgers-Fisher equation (TF-GBF). The TF-GBF is transformed into a nonlinear…
This work proposes a deep learning-based emulator for the efficient computation of the coupled viscous Burgers' equation with random initial conditions. In a departure from traditional data-driven deep learning approaches, the proposed…
We extend Robust Optimization to fractional programming, where both the objective and the constraints contain uncertain parameters. Earlier work did not consider uncertainty in both the objective and the constraints, or did not use Robust…
In the context of adjoint-based optimization, nonlinear conservation laws pose significant problems regarding the existence and uniqueness of both direct and adjoint solutions, as well as the well-posedness of the problem for sensitivity…