相关论文: An approximate solution of the MHD Falkner-Skan fl…
The Hermite pseudospectral method is applied to solve the Navier-Stokes equations on a two-dimensional infinite domain. The feature of Hermite function allows us to adopt larger time steps than other spectral methods, but also leads to some…
In this paper we propose a collocation method for solving some well-known classes of Lane-Emden type equations which are nonlinear ordinary differential equations on the semi-infinite domain. They are categorized as singular initial value…
This paper deals with the two-dimensional incompressible, laminar, steady-state boundary layer equations.First, we determine a family of velocity distributions outside the boundary layer such that these problems may have similarity…
We demonstrate that the asymptotic approximant applied to the Blasius boundary layer flow over a flat plat (Barlow et al., 2017 Q. J. Mech. Appl. Math., 70(1): 21-48) yields accurate analytic closed-form solutions to the Falkner-Skan…
The present work deals with the two-dimensional incompressible,laminar, steady-state boundary layer equations. First, we determinea family of velocity distributions outside the boundary layer suchthat these problems may have similarity…
In this paper, we propose Hermite collocation method for solving Thomas-Fermi equation that is nonlinear ordinary differential equation on semi-infinite interval. This method reduces the solution of this problem to the solution of a system…
In this paper, we propose a numerical method to approximate the solution of partial differential equations in irregular domains with no-flux boundary conditions by means of spectral methods. The main features of this method are its…
This paper details the development and application of an $h$-adaptive finite element method for the numerical solution of the \textit{Falkner-Skan equation}. A posteriori error estimation governs the adaptivity of the mesh, specifically the…
We study an approximation method to solve nonlinear multi-term fractional differential equations with initial conditions or boundary conditions. First, we transform the nonlinear multi-term fractional differential equations with initial…
We present a new solver for coupled nonlinear elliptic partial differential equations (PDEs). The solver is based on pseudo-spectral collocation with domain decomposition and can handle one- to three-dimensional problems. It has three…
In this paper, a new deep-learning architecture for solving the non-linear Falkner-Skan equation is proposed. Using Legendre and Chebyshev neural blocks, this approach shows how orthogonal polynomials can be used in neural networks to…
A systematic search for the Lie point symmetries admitted by the steady hydromagnetic two-dimensional incompressible viscous flow boundary layer equation and associated boundary conditions is performed. Unlike previous works, the specific…
In this paper we compare three different orthogonal systems in $\mathrm{L}_2(\mathbb{R})$ which can be used in the construction of a spectral method for solving the semi-classically scaled time dependent Schr\"odinger equation on the real…
We introduce a general third order non-linear autonomous ODE which covers many ODEs coming from boundary layer problems, like the Falkner-Skan equation and the Cheng-Minkowycz equation. Using Wiman-Valiron theory and complex analytic…
We explain how to use smooth bivariate splines of arbitrary degree to solve the exterior Helmholtz equation based on a Perfectly Matched Layer (PML) technique. In a previous study (cf. [26]), it was shown that bivariate spline functions of…
We apply pseudo-spectral methods to integrate functional flow equations with high accuracy, extending earlier work on functional fixed point equations \cite{Borchardt:2015rxa}. The advantages of our method are illustrated with the help of…
A multiscale numerical method is proposed for the solution of semi-linear elliptic stochastic partial differential equations with localized uncertainties and non-linearities, the uncertainties being modeled by a set of random parameters. It…
In this paper we propose a Lagrangian method for solving Lane-Emden equation which is a nonlinear ordinary differential equation on semi-infinite interval. This approach is based on a Modified generalized Laguerre functions Lagrangian…
In this paper, the fractional order of rational Bessel functions collocation method (FRBC) to solve Thomas-Fermi equation which is defined in the semi-infinite domain and has singularity at $x = 0$ and its boundary condition occurs at…
In this paper, we mainly discuss the convergence behavior of diffuse domain method (DDM) for solving semilinear parabolic equations with Neumann boundary condition defined in general irregular domains. We use a phasefield function to…