相关论文: Scaling Invariance and the Iterative Transformatio…
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 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.…
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…
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…
Coefficient inverse problems related to identifying the right-hand side of an equation with use of additional information is of interest among inverse problems for partial differential equations. When considering non-stationary problems,…
We present a stochastic numerical method for solving fully non-linear free boundary problems of parabolic type and provide a rate of convergence under reasonable conditions on the non-linearity.
In the present work, we consider a nonlinear inverse problem of identifying the lowest coefficient of a parabolic equation. The desired coefficient depends on spatial variables only. Additional information about the solution is given at the…
In this paper we continue to study a non-local free boundary problem arising in financial bubbles. We focus on the parabolic counterpart of the bubble problem and suggest an iterative algorithm which consists of a sequence of parabolic…
We define a non-iterative transformation method for Blasius equation with moving wall or surface gasification. The defined method allows us to deal with classes of problems in boundary layer theory that, depending on a parameter, admit…
In this paper we define a non-iterative transformation method for an Extended Blasius Problem. The original non-iterative transformation method, which is based on scaling invariance properties, was defined for the classical Blasius problem…
We propose in this work a novel iterative direct sampling method for imaging moving inhomogeneities in parabolic problems using boundary measurements. It can efficiently identify the locations and shapes of moving inhomogeneities when very…
The scaling of the exact solution of a hyperbolic balance law generates a family of scaled problems in which the source term does not depend on the current solution. These problems are used to construct a sequence of solutions whose…
The first contribution of this paper is the extension of the non-iterative transformation method, proposed by T\"opfer more than a century ago and defined for the numerical solution of the Blasius problem, to a Blasius problem with extended…
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…
This paper is concerned with two examples on the application of the free boundary formulation to BVPs on a semi-infinite interval. In both cases we are able to provide the exact solution of both the BVP and its free boundary formulation.…
This work deals with the problem of choosing a time step for the numerical solution of boundary value problems for parabolic equations. The problem solution is derived using the fully implicit scheme, whereas a time step is selected via…
We show that Boundary Control method, a method for hyperbolic inverse problems, is also capable of dealing directly with certain classes of elliptic and parabolic Inverse Boundary Value Problems; thus pointing towards Boundary Control…
We assess the applicability and efficiency of time-adaptive high-order splitting methods applied for the numerical solution of (systems of) nonlinear parabolic problems under periodic boundary conditions. We discuss in particular several…
Solving parabolic optimal control problems can be inherently challenging in the field of science and engineering, especially with constraints on the nonsmooth distributed control. Motivated by the extensive applicability of the alternating…