Related papers: Exact analytical solution for the Sakiadis boundar…
The Sakiadis boundary layer induced by a moving wall in a semi-infinite fluid domain is a fundamental laminar flow field relevant to high speed coating processes. This work provides an analytical solution to the boundary layer problem for…
In a transformation method the numerical solution of a given boundary value problem is obtained by solving one or more related initial value problems. This paper is concerned with the application of the iterative transformation method to…
We consider the problem of convective heat transfer across the laminar boundary-layer induced by an isothermal moving surface in a Newtonian fluid. In previous work (Barlow, Reinberger, and Weinstein, 2024, \textit{Physics of Fluids},…
We examine the power series solutions of two classical nonlinear ordinary differential equations of fluid mechanics that are mathematically related by their large-distance asymptotic behaviors in semi-infinite domains. The first problem is…
Blasius boundary layer solution is a Maclaurin series expansion of the function \(f(\eta)\), which has convergence problems when evaluating for higher values of \(\eta\) due to a singularity present at \(\eta\approx-5.69\). In this paper we…
In a transformation method, the numerical solution of a given boundary value problem is obtained by solving one or more related initial value problems. Therefore, a transformation method, like a shooting method, is an initial value method.…
A compact and accurate solution method is provided for problems whose infinite power series solution diverges and/or whose series coefficients are only known up to a finite order. The method only requires that either the power series…
A new highly accurate algorithm for the solution of the Falkner-Skan equation of boundary layer theory is presented. The algorithm, based on a Maclaurin series representation, finds its coefficients from recurrence. In addition,…
We construct a perfectly matched absorbing layer for stationary Schrodinger equation with analytic slowly decaying potential in a periodic structure. We prove the unique solvability of the problem with perfectly matched layer of finite…
We use a recently developed method \cite{Costinetal}, \cite{Dubrovin} to find accurate analytic approximations with rigorous error bounds for the classic similarity solution of Blasius of the boundary layer equation in fluid mechanics, the…
We develop a new semi-analytical method for solving multilayer diffusion problems with time-varying external boundary conditions and general internal boundary conditions at the interfaces between adjacent layers. The convergence rate of the…
We present a fully analytic approach for evaluating boundary integrals in two dimensions for Smoothed Particle Hydrodynamics (SPH). Conventional methods often rely on boundary particles or wall re-normalization approaches derived from…
Some approach to the solution of boundary value problems for finding functions, which are analytical in a wedge, is proposed. If the ratio of the angle at the wedge vertex to a number \pi is rational, then the boundary value problem is…
In this paper, within scaling invariance theory, we define and apply to the numerical solution of a similarity boundary layer model an iterative transformation method. The boundary value problem to be solved depends on a parameter and is…
We provide an algorithm, running in polynomial time in the number of vertices, computing the unique solution to the biased infinity Laplacian Boundary Problem on finite graphs. The algorithm is based on the general outline and approach…
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…
For the problems indicated in the title, a further development of a new approach (different from those applied before) is given. A basic problem under consideration arises in viscous incompressible fluid dynamics and describes self-similar…
The boundary layer of a finite domain [a, b] covers mesoscopic lateral neighbourhoods, inside [a, b], of the endpoints a and b. The correct diagnostic of the integrand behaviour at a and b, based on its sampling inside the boundary layer,…
Boundary integral equations are an efficient and accurate tool for the numerical solution of elliptic boundary value problems. The solution is expressed as a layer potential; however, the error in its evaluation grows large near the…
This paper is concerned with an initial and boundary value problem of the one-dimensional planar MHD equations for viscous, heat-conducting, compressible, ideal polytropic fluids with constant transport coefficients and large data. The…