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A Non-Iterative Transformation Method Applied to Boundary-Layer Flows of Non-Newtonian Fluids Past a Flat Plate
Riccardo Fazio
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 p…
An Iterative Transformation Method for a Similarity Boundary Layer Model
Riccardo Fazio
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…
A Non-Iterative Transformation Method for Boundary-Layer with Power-Law Viscosity for Newtonian Fluids
Riccardo Fazio
In this paper, we have defined and applied a non-ITM to an extended Blasius problem describing a 2D laminar boundary-layer with power-law viscosity for Newtonian fluids. For a part…
Existence and Uniqueness of BVPs Defined on Semi-Infinite Intervals: Insight from the Iterative Transformation Method
Riccardo Fazio
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…
Numerical Transformation Methods for a Moving-Wall Boundary Layer Flow of a Rarefied Gas Free Stream over a Moving Flat Plate
Riccardo Fazio
The first contribution of this paper is the extension of the non-iterative transformation method, proposed by Töpfer more than a century ago and defined for the numerical solution…
Free Boundary Formulation for Boundary Value Problems on Semi-Infinite Intervals: An up to Date Review
Riccardo Fazio
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 convenien…
Free Boundary Formulations for two Extended Blasius Problems
Riccardo Fazio
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 gov…
A Front Fixing Implicit Finite Difference Method for the American Put Options Model
Riccardo Fazio, Alessandra Insana, Alessandra Jannelli
In this paper, we present an implicit finite difference method for the numerical solution of the Black-Scholes model of American put options without dividend payments. We combine t…
A Non-Iterative Transformation Method for an Extended Blasius Problem
Riccardo Fazio
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 invarianc…
The Non-Iterative Transformation Method
Riccardo Fazio
The Blasius flow is the idealized flow of a viscous fluid past an infinitesimally thick, semi-infinite flat plate. The definition of a non-iterative transformation method for the c…
A Non-Standard Finite Difference Scheme for MHD Boundary Layer Fluid Flow
Riccardo Fazio, Alessandra Jannelli
This paper deals with a non-standard finite difference scheme defined on a quasi-uniform mesh for approximate solutions of the MHD boundary layer flow of an incompressible fluid pa…
A Non-Iterative Transformation Method for a Class of Free Boundary Value Problems Governed by ODEs
Riccardo Fazio, Salvatore Iacono
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 valu…
A Finite Difference Method on Quasi-uniform Mesh for Time-Fractional Advection-Diffusion Equations with Source Term
Riccardo Fazio, Alessandra Jannelli
The present paper deals with the numerical solution of time-fractional advection-diffusion equations involving the Caputo derivative with source term by means of an unconditionally…
A Posteriori Error Estimator for a Non-Standard Finite Difference Scheme Applied to BVPs on Infinite Intervals
Riccardo Fazio, Alessandra Jannelli
In this paper, we present a study of an a posteriori estimator for the discretization error of a non-standard finite difference scheme applied to boundary value problems defined on…
A Non-Iterative Transformation Method for Blasius Equation with Moving Wall or Surface Gasification
Riccardo Fazio
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 boun…
Perpetual American Put Option: an Error Estimator for Non-Standard Finite Difference Scheme
Riccardo Fazio
In this paper we present a MATLAB version of a non-standard finite difference scheme for the numerical solution of the perpetual American put option models of financial markets. Th…
The Iterative Transformation Method for the Sakiadis Problem
Riccardo Fazio
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…
Free Boundary Formulation for BVPs on a Semi-Infinite Interval and Non-Iterative Transformation Methods
Riccardo Fazio
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 so…
A Non-Iterative Transformation Method for Newton's Free Boundary Problem
Riccardo Fazio
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 variation…
Numerical Methods for a Nonlinear BVP Arising in Physical Oceanography
Riccardo Fazio, Alessandra Jannelli
In this paper we report and compare the numerical results for an ocean circulation model obtained by the classical truncated boundary formulation, the free boundary approach and a…
Blasius Problem and Falkner-Skan model: Töpfer's Algorithm and its Extension
Riccardo Fazio
In this paper, we review the so-called Töpfer algorithm that allows us to find a non-iterative numerical solution of the Blasius problem, by solving a related initial value problem…
Scaling Invariance and the Iterative Transformation Method for a Class of Parabolic Moving Boundary Problems
Riccardo Fazio
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.…
Finite difference schemes on quasi-uniform grids for Bvps on infinite intervals
Riccardo Fazio, Alessandra Jannelli
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 fi…