Related papers: Free Boundary Formulation for BVPs on a Semi-Infin…
In this paper, we propose a review of the free boundary formulation for BVPs defined on semi-infinite intervals. The main idea and theorem are illustrated, for the reader convenience, by using a class of second-order BVPs. Moreover, we are…
This work is concerned with the existence and uniqueness of boundary value problems defined on semi-infinite intervals. These kinds of problems seldom admit exactly known solutions and, therefore, the theoretical information on their…
A definition of invariance in Lie's sense for a boundary value problem (BVP) with the basic evolution differential equations is proposed. A problem of group classification at a wide class of BVPs parameterized by arbitrary elements 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…
The aim of this work is to point out that the class of free boundary problems governed by second order autonomous ordinary differential equations can be transformed to initial value problems. Interest in the numerical solution of free…
In book II of Newton's "Principia Mathematica" of 1687 several applicative problems are introduced and solved. There, we can find the formulation of the first calculus of variations problem that leads to the first free boundary problem of…
In this work we propose a novel approach to investigate boundary value problems (BVPs) for fully third order differential equations. It is based on the reduction of BVPs to operator equations for the nonlinear terms but not for the…
A class of (1+1)--dimensional nonlinear boundary value problems (BVPs), modeling the process of melting and evaporation of solid materials, is studied by means of the classical Lie symmetry method. New definition of invariance in Lie's…
In this work we present a method, based on the use of Bernstein polynomials, for the numerical resolution of some boundary values problems. The computations have not need of particular approximations of derivatives, such as finite…
A new definition of Lie invariance for nonlinear multi-dimensional boundary value problems (BVPs) is proposed by the generalization of known definitions to much wider classes of BVPs. The class of (1+3)-dimensional nonlinear BVPs of the…
In this paper, we define a non-iterative transformation method for boundary-layer flows of non-Newtonian fluids past a flat plate. The problem to be solved is an extended Blasius problem depending on a parameter. This method allows us to…
In this paper we apply a scaling invariance analysis to reduce a class of parabolic moving boundary problems to free boundary problems governed by ordinary differential equations. As well known free boundary problems are always non-linear…
We derive new boundary conditions and implementation procedures for nonlinear initial boundary value problems (IBVPs) with non-zero boundary data that lead to bounded solutions. The new boundary procedure is applied to nonlinear IBVPs in…
In this paper, we consider a boundary value problem (BVP) for a fourth order nonlinear functional integro-differential equation. We establish the existence and uniqueness of solution and construct a numerical method for solving it. We prove…
In this study we are concerned with a class of generalized BVP' s consisting of eigendependent boundary conditions and supplementary transmission conditions at finite number interior points. By modifying some techniques of classical…
In this paper, we have defined the free boundary formulation for two extended Blasius problems. These problems are of interest in boundary layer theory and are deduced from the governing partial differential equations by using appropriate…
An iterative solution method for fully nonlinear boundary value problems governing self-similar flows with a free boundary is presented. Specifically, the method is developed for application to water entry problems, which can be studied…
A first-order ordinary differential equation, solved with respect to derivative, is considered. It's right-hand side is defined and continuous on the set, consisting of a connected open subset of a two-dimensional Euclidean space and a part…
The classical numerical treatment of boundary value problems defined on infinite intervals is to replace the boundary conditions at infinity by suitable boundary conditions at a finite point, the so-called truncated boundary. A truncated…
The purpose of this survey chapter is to present a transformation technique that can be used in analysis and numerical computation of the early exercise boundary for an American style of vanilla options that can be modelled by class of…