Related papers: Approximate Solution of Kuramoto-Sivashinsky Equat…
We discuss a numerical scheme to solve the continuum Kardar-Parisi-Zhang equation in generic spatial dimensions. It is based on a momentum-space discretization of the continuum equation and on a pseudo-spectral approximation of the…
A variationally improved Sturmian approximation for solving time-independent Schr\"odinger equation is developed. This approximation is used to obtain the energy levels of a quartic anharmonic oscillator, a quartic potential, and a Gaussian…
For a system of partial differential equations that has an extended Kovalevskaya form, a reduction procedure is presented that allows one to use a local (point, contact, or higher) symmetry of a system and a symmetry-invariant conservation…
We present an exponentially convergent numerical method to approximate the solution of the Cauchy problem for the inhomogeneous fractional differential equation with an unbounded operator coefficient and Caputo fractional derivative in…
The conformable time fractional Jimbo-Miwa and Zakharov-Kuznetsov equations are solved by the generalized form of the Kudryashov method. A simple compatible wave transformation is employed to reduce the dimension of the equations to one.…
A numerical method for approximating weak solutions of an aggregation equation with degenerate diffusion is introduced. The numerical method consists of a stabilized finite element method together with a mass lumping technique and an extra…
We prove existence of solutions to the Kuramoto-Sivashinsky equation with low-regularity data, in function spaces based on the Wiener algebra and in pseudomeasure spaces. In any spatial dimension, we allow the data to have its…
An approximate method is proposed for the recovery of a compactly supported spherically-symmetric potential from the set of fixed-energy phase-shifts known for all angular momenta. The method reduces the inverse scattering problem to a…
In this paper, we present analytic-approximate solution of a fractional Zakharov-Kuznetsov equation by means of perturbation-iteration algorithm (PIA) and residual power series method (RSPM). Basic definitions of fractional derivatives are…
The conserved Kuramoto-Sivashinsky (CKS) equation, u_t = -(u+u_xx+u_x^2)_xx, has recently been derived in the context of crystal growth, and it is also strictly related to a similar equation appearing, e.g., in sand-ripple dynamics. We show…
The Schwinger-Dyson equation of fermion self-energy in the linearization approximation is solved exactly in a theory with gauge and effective four-fermion interactions. Different expressions for the indepedent solutions which respectively…
Recently, a new fractional derivative called the conformable fractional derivative is given which is based on the basic limit definition of the derivative in [1]. Then, the fractional versions of chain rules, exponential functions,…
This paper deals with approximate solutions of an optimization problem with interval-valued objective function. Four types of approximate solution concepts of the problem are proposed by considering the partial ordering $LU$ on the set of…
In this paper, we propose a method to approximate the Gaussian function on ${\mathbb R}$ by a short cosine sum. We generalise and extend the differential approximation method proposed in [4, 40] to approximate $\mathrm{e}^{-t^{2}/2\sigma}$…
The objective of this paper is to present an approximation formula for the Katugampola fractional integral, that allows us to solve fractional problems with dependence on this type of fractional operator. The formula only depends on…
A new method to remove the stiffness of partial differential equations is presented. Two terms are added to the right-hand-side of the PDE : the first is a damping term and is treated implicitly, the second is of the opposite sign and is…
We prove strong convergence of a semi-discrete finite difference method for the KdV and modified KdV equations. We extend existing results to non-smooth data (namely, in $L^2$), without size restrictions. Our approach uses a fourth order…
The Inverse Problem for the estimation of a point-wise approximation error occurring at the discretization and solving of the system of partial differential equations is addressed. The set of the differences between the numerical solutions…
This paper studies the numerical methods to approximate the solutions for a sort of McKean-Vlasov neutral stochastic differential delay equations (MV-NSDDEs) that the growth of the drift coefficients is super-linear. First, We obtain that…
Many physical systems are modeled by nonlinear parabolic differential equations, such as the Kuramoto-Sivashinsky (KS) equation. In this paper, the existence of a concurrent optimal controller and actuator design is established for…