An Iterative Transformation Method for a Similarity Boundary Layer Model.
Preprint, 2025.
A Non-Iterative Transformation Method Applied to Boundary-Layer Flows of Non-Newtonian Fluids.
Submitted to: J. Comput. Sci., 2025.
Free Boundary Formulation for Boundary Value Problems on Semi-Infinite Intervals: An up to Date Review.
Accepted by: Math. Meth. Appl. Sci., 2025.
Numerical Transformation Mehtods for a Moving-Wall Boundary Layer Flow of a Rarefied Gas Free Stream over a Moving Flat Plate.
Mathematics, 13, (2025) 601.
Free Boundary Formulation of two Extended Blasius Problems.
Int. J. Non-Linear Mech., 153 (2023) 104423.
A Non-Iterative Transformation Method for Boundary-Layer with Power-Law Viscosity for non-Newtonian Fluids.
Calcolo, 59, 43, 2022.
A Front Fixing Implicit Finite Difference Method for the American Put Option Model.
Joint work with: A. Jannelli and A. Insana. Math. Comput. Appl., 1, 0, 2021.
A Non-Standard Finite Difference Scheme for Magneto-Hydro-Dynamics Boundary Layer Flow of an Incompressible Fluid Past a Flat Plate.
Joint work with A. Jannelli, Math. Comput. Appl., 26, 22, 2021.
Existence and Uniqueness of BVPs Defined on Infinite Intervals: Insight from the Iterative Transformation Method.
Math. Comput. Appl., 26, 18, 2021.
Perpetual American Put Option: an Error Estimator for a Non-Standard Finite Difference Scheme.
Appl. Math. E-Notes, 21, 282-290, 2021.
A Non-Iterative Transformation Method for an Extended Blasius Problem.
Math. Meth. Appl. Sci., 44, 1996-2001, 2021.
Scaling Invariance and Numerical Transformation Methods: A Unifying Framework.
Appl Engin. Sci., 4, 100024, 2020.
OCTAVE per l'Economia e la Finanza. TGBook Ed., Sandrigo, 2020.
American Put Option: Richardson's extrapolation and a Posteriori Error Estimator for a Front-Fixing Finite Difference Scheme.
Appl. Math. E-Notes, 20,445-457, 2020.
The Iterative Transformation Method. Int. J. Nonlinear Mech., 116, 181-194, 2019.
The Non-Iterative Transformation Method. Int. J. Nonlinear Mech., 114, 41-48, 2019.
Numerical study on gas flow through a micro-nano porous medium based on finite difference schemes on
quasi-uniform grids. Joint work with A. Jannelli and T. Rotondo. Int. J. Non-Linear Mech., 105, 186-191, 2018.
Two finite difference methods for a nonlinear BVP arising in physical oceanography. Joint work with A. Jannelli. AAPP | Atti della Accademia Peloritana dei Pericolanti, 96, A3, 2018.
BVPs on infinite intervals: A test problem, a nonstandard finite
difference scheme and a posteriori error estimator. Joint work with A. Jannelli, Math. Meth. Appl. Sci., 40, 6285-6294, 2017. Well-posed initial conditions and numerical methods for one-dimensional models of liquid dynamics in a horizontal capillary.
Joint work with A. Jannelli. Comput. Appl. Math., 36, 903-913, 2017. Front fixing finite difference schemes for American put options model. Joint work with A. Insana and
A. Jannelli, International Conference of Numerical Analysis and Applied Mathematics 2015 (ICNAAM 2015)
AIP Conf. Proc. 1738, 480123-1--480123-4, 2016. A Non-Iterative Transformation Method for Blasius Equation with Moving Wall or
Surface Gasification, Int. J. Non-Linear Mech., 78, 156-159, 2016. The Iterative Transformation Method for the
Sakiadis Problem, Comput. & Fluids, 106, 196-200, 2015. Free Boundary Formulation for BVPs on a Semi-infinite
Interval and Non-iterative Transformation Methods.
Acta Appl. Math., 140, 27-42, 2015. A Posteriori Error Estimator for a Front-Fixing
Finite Difference Scheme for American Options.
WCE2015, London June 30 - July 3, 2015. Metodi Numerici per Problemi ai Valori Iniziali, TGBook Ed., Sandrigo, 2014.Elementi di Analisi Numerica, TG Book ed., 2014.Finite Difference Schemes on Quasi-Uniform
Grids for BVPs on Infinite Intervals. Joint work with A. Jannelli. J. Comput. Appl. Math., 269, 14-23, 2014. A Non-Iterative Transformation Method for Newton's Free Boundary Problem.
Int. J. Non-Linear Mech., 59, 23-27, 2014. An Analytical and Numerical Study of Liquid
Dynamics in a 1D Capillary under Entrapped Gas Action. Joint work with S. Iacono. Math. Meth. Appl. Sci., 37, 2923-2933, 2014.
Quasi-uniform Grids and Ad Hoc Finite Difference Schemes for BVPs on Infinite Intervals.
Joint work with A. Jannelli. ENUMATH 2013. Blasius Problem and Falkner-Skan model: Toepfer's Algorithm
and its Extension. Computers Fluids, 73, 202-209, 2013. Scaling Invariance and the Iterative Transformation Method
for a Class of Parabolic Moving Boundary Problems. Int. J. Non-Linear Mech., 50, 136-140, 2013. Extended Scaling Invariance of
One-dimensional Models of Liquid Dynamics in a Horizontal Capillary. Joint work with
S. Iacono, A. Jannelli, G. Cavaccini, and V. Pianese. Math. Meth. Appl. Sci., 35, 935-942, 2012. A
Central Schemes and Second Order Boundary Conditions for 1D Interface and Piston Problems in Lagrangian Coordinates. Joint work with G.
Russo. Commun. Comput. Phys., 8, 797-822, 2010.An Instance of Failure for the MATLAB Explicit ODE45 Solver. Proceedings ICAEM 2010. London, June 30 - July 2, 2010. On the Moving Boundary Formulation for Parabolic Problems on Unbounded Domains. Joint
work with S. Iacono. Int. J. Comput. Math., 87, 186-198, 2010. On the Equivalence of Non-Iterative
Transformation Methods Based on Scaling and Spiral Groups. Joint work with
S. Iacono. Math. Meth. Appl. Sci., 30, 585-591, 2010. One-dimensional Mathematical and Numerical
Modeling of Liquids Dynamics in a Horizontal Capillary. Joint
work with G. Cavaccini, V. Pianese, S. Iacono, and A. Jannelli.
J. Comput. Meth. Sci. Eng., 9, 3-16, 2009.
Numerical Transformation Methods: Blasius Problem and its Variants.
Appl. Math. Comput., 215, 1513-1521, 2009.Second Order
Positive Schemes by means of Flux Limiters for the Advection Equation.
Joint work with A. Jannelli. IAENG Int. J. Appl. Math., 2009. Pseudo-Spectral Methods
for Linear Advection and Dispersive Problems. Joint work with
S. Iacono. IAENG Int. J. Appl. Math., 2009.
Second Order Numerical Operator Splitting for 3D Advection-Diffusion-Reaction Models.
Joint work with A. Jannelli. Proceedings ENUMATH 2009. Liquid Penetrant
Testing: Industrial Process. Joint work with G. Caturano, G. Cavaccini, A. Ciliberto, and V. Pianese,
Communications to SIMAI Congress, 2009. Liquid Dynamics in
a Horizontal Capillary: Extended Similarity Analysis. Joint
work with S. Iacono, A. Jannelli, G. Cavaccini, and V. Pianese,
to appear: Communications to SIMAI Congress, 2009. Ill and Well-Posed
One-Dimensional Models of Liquid Dynamics in a Horizontal Capillary. Joint
work with A. Jannelli, Communications to SIMAI Congress, 2009. On Translation
Groups and Non-iterative Transformation Methods. Joint work with S. Iacono, Communications to SIMAI Congress, 2009. Transformation
Methods for the Blasius Problem and its Recent Variants.
Proceedings ICAEM 2008. London, July 2-4, 2008. Scaling and Spiral
Equivalence from a Numerical Viewpoint. Joint work with
S. Iacono. Proceedings ICAEM 2008. London, July 2-4, 2008. Numerical Scaling Invariance
Applied to the van der Pol Model . Acta
Appl. Math., 104, 107-114, 2008. A Two Immiscible
Liquids Penetration Model for Surface-Driven Capillary Flows. Joint
work with S. Iacono, A. Jannelli, G. Cavaccini, and V. Pianese.
Presented at the ICIAM 2007. On the Moving Boundary
Formulation for Parabolic Problems on Unbounded Domains. Joint
work with S. Iacono. Presented at the ICIAM 2007. Invited talk at WASCOM07
Congress, Scicli, June 30 -- July 7, 2007, joint work with
A. Jannelli. Local Error
Reduction for First Order Implicit Pseudo-Spectral Methods Applied to
Linear Advection Models. Joint work with Alessandra Jannelli and Salvatore Iacono. Mathematical and Numerical
Modeling of Liquids Dynamics in a Horizontal Capillary. Joint
work with G. Cavaccini, V. Pianese, S. Iacono, and A. Jannelli.
Presented at the ICCMSE 2006. Mathematical and Numerical
Modeling for a Bio-Chemical Aquarium. Joint work with
A. Jannelli. Appl. Math. Comp., 174, 1370-1383, 2006
Implicit Pseudo-Spectral Methods for Dispersive and Wave Propagation Problems.
Joint work with A. Jannelli. Communications to SIMAI Congress, 2006. Adaptive Stiff Solvers at Low
Accuracy and Complexity. Joint work with A. Jannelli,
J. Comput. Appl. Math., 191, 246-258, 2006. Numerical Analysis
for Advection-Diffusion-Reaction Models in 3D. Joint work
with A. Jannelli, Poster presented at NAC2005, Numerical
Analysis: the State of the Art, Cosenza, May 21-25, 2005. Moving-Mesh
Methods for One-dimensional Hyperbolic Problems Using CLAWPACK.
Joint work with Randy J. LeVeque. Comp. Math. Appl., 45, 273-298, 2003 A Free Boundary Approach and
Keller's Box Scheme for Boundary Value Problems on Infinite Intervals. Int. J. Comput. Math., 80, 1549-1560, 2003.
Stiffness in Numerical
Initial Value Problems: A and L-Stability of Numerical Methods Int. J. Math. Ed. Sci. Tech., 32, 752-760, 2001.
MATLAB files available: ALstab.zip
The Iterative Transformation Method:
Numerical Solution of One-Dimensional Parabolic Moving Boundary Problems. 78, 213-223, Int. J. Comput. Math., 2001.
Comparison of Two
Conservative Schemes for Hyperbolic Interface Problems.
Presented at the ENUMATH 2001 (Fourth European Conference on Numerical
Mathematics), Ischia, 23-28 July 2001 Similarity and Numerical
Analysis of a Singular Moving Boundary Hyperbolic Problem.
Presented at the 11th ECMI (the European Consortium for Mathematics in
Industry) Conference, Torre Normanna -- Palermo, 26-30 September 2000. A Survey on Free Boundary
Identification of the Truncated Boundary in Numerical BVPs on Infinite
Intervals. Presented at the ICCAM 2000 Conference, Leuven,
17-21 July 2000. J. Comput. Appl. Math., 140, 331-344, 2002. A
3D Mathematical Model for the Prediction of Mucilage Dynamics.
Joint work with A. Jannelli and D. Ambrosi. Presented at
the AMIF (Applied Mathematics for Industrial) Flows 2nd Inter.
Conference, Il Ciocco, 12-14 October 2000. A Lagrangian Central
Scheme for Multi-Fluid Flows. Joint work with G. Russo.
Presented at the Eighth International Conference on Hyperbolic
Problems, Teory, Numerics, Applications, Magdeburg, 28 Febbraio - 3
Marzo, 2000. Numerical Applications of the
Scaling Concept. Acta Appl. Math., 55, 1-25, 1999.
For the Bibliography print the sc-gita.pdf file
and use the BIB files: sc-gita.bibsc-gita2.bib
right click and save as ... A Similarity Approach to the
Numerical Solution of Free Boundary Problems. SIAM Rev., 40, 616-635, 1998 A Numerical Test for the Existence and Uniqueness
of Free Boundary Problems. Appl. Anal., 66, 89-100, 1997. A Novel Approach to the
Numerical Solution of Boundary Value Problems on Infinite Intervals. SIAM J. Numer. Anal., 33, 1473-1483, 1996. The Falkner-Skan Equation:
Numerical Solutions within Group Invariance Theory. Calcolo, 31, 115-124, 1994. An Implicit Difference Scheme for a Moving
Boundary Hyperbolic Problem. Joint work with David J. Evans, Appl. Numer. Math., 12, 485-496, 1993. A Moving Boundary Hyperbolic Problem for a Stress Impact
in a Bar of Rate-Type Materials. Wave Motion, 16, 299-305, 1992. Numerical Length Estimation
for Tubular Flow Reactors. J. Comput. Appl. Math., 41, 313-321, 1992. The Blasius Problem Formulated
as a Free Boundary Value Problem. Acta Mech, 95, 1-7, 1992. The Iterative Transformation Method
and Length Estimation for Tubular Flow Reactors. Appl. Math. Comput., 42, 105-110, 1991. Normal Variables Transformation Methods Applied to Free
Boundary Value Problems. Int. J. Comput. Math., 37, 189-199, 1990. Similarity and Numerical Analysis for Free
Boundary Value Problems. Joint work with David J. Evans, Int. J. Comput. Math., 31, 215-220, 1990. A Nonlinear Hyperbolic Free Boundary Value
Problem. Acta Mech., 81, 221-226, 1990. 
By Riccardo Fazio. Last modified: October 21, 2025.