scholarly journals Umbral interpolation

2016 ◽  
Vol 99 (113) ◽  
pp. 165-175 ◽  
Author(s):  
Francesco Costabile ◽  
Elisabetta Longo
Keyword(s):  
Interpolation Problem ◽  
Truncation Error ◽  
Linear Interpolation ◽  
General Linear ◽  
Numerical Examples ◽  
Sheffer Polynomials

A general linear interpolation problem is posed and solved. This problem is called umbral interpolation problem because its solution can be expressed by a basis of Sheffer polynomials. The truncation error and its bounds are considered. Some examples are discussed, in particular generalizations of Abel-Gontscharoff and central interpolation are studied. Numerical examples are given too.

scholarly journals An algebraic exposition of umbral calculus with application to general linear interpolation problem: A survey

2014 ◽  
Vol 96 (110) ◽  
pp. 67-83 ◽  
Author(s):  
Francesco Costabile ◽  
Elisabetta Longo
Keyword(s):  
Interpolation Problem ◽  
Linear Interpolation ◽  
Umbral Calculus ◽  
General Linear ◽  
Numerical Examples ◽  
Polynomial Sequences ◽  
Sheffer Sequences ◽  
Determinantal Form ◽  
Systematic Exposition ◽  
Sheffer Polynomial

A systematic exposition of Sheffer polynomial sequences via determinantal form is given. A general linear interpolation problem related to Sheffer sequences is considered. It generalizes many known cases of linear interpolation. Numerical examples and conclusions close the paper.

scholarly journals Lidstone–Euler Second-Type Boundary Value Problems: Theoretical and Computational Tools

2021 ◽  
Vol 18 (5) ◽  
Author(s):  
Francesco Aldo Costabile ◽  
Maria Italia Gualtieri ◽  
Anna Napoli
Keyword(s):  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Existence And Uniqueness ◽  
Interpolation Problem ◽  
Boundary Value ◽  
Computational Tools ◽  
Numerical Examples ◽  
Odd Order ◽  
Uniqueness Of The Solution ◽  
Type Boundary

AbstractGeneral nonlinear high odd-order differential equations with Lidstone–Euler boundary conditions of second type are treated both theoretically and computationally. First, the associated interpolation problem is considered. Then, a theorem of existence and uniqueness of the solution to the Lidstone–Euler second-type boundary value problem is given. Finally, for a numerical solution, two different approaches are illustrated and some numerical examples are included to demonstrate the validity and applicability of the proposed algorithms.

Research on Contour Interpolation in Reverse Engineering

2012 ◽  
Vol 170-173 ◽  
pp. 3304-3307
Author(s):  
Hong Liang Wang ◽  
Hai Fei Ding ◽  
Jin Qi Wang
Keyword(s):  
Rapid Prototyping ◽  
Reverse Engineering ◽  
Interpolation Problem ◽  
Minimum Distance ◽  
Linear Interpolation ◽  
Contour Interpolation ◽  
Vehicle Engine

In reverse engineering and rapid prototyping, several intermediate contours interpolated between adjacent two-layer ICT slice are needed to meet the requirement of rapid prototyping. A method of linear interpolation based on minimum distance is adopted in this paper. On the basis of the research on interpolation problem between single contours, some researches on the interpolation problem of multiply contours was done in this paper. Satisfactory results are attained by the experiments of a vehicle engine.

scholarly journals Application of Fuzzy Finite Difference Scheme for the Non-homogeneous Fuzzy Heat Equation

2021 ◽  
Author(s):  
Samaneh Zabihi ◽  
reza ezzati ◽  
F Fattahzadeh ◽  
J Rashidinia
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Heat Equation ◽  
Difference Scheme ◽  
Difference Method ◽  
Taylor Expansion ◽  
Truncation Error ◽  
Initial Boundary ◽  
Convergence Conditions ◽  
Numerical Examples

Abstract A numerical framework based on fuzzy finite difference is presented for approximating fuzzy triangular solutions of fuzzy partial differential equations by considering the type of $[gH-p]-$differentiability. The fuzzy triangle functions are expanded using full fuzzy Taylor expansion to develop a new fuzzy finite difference method. By considering the type of gH-differentiability, we approximate the fuzzy derivatives with a new fuzzy finite-difference. In particular, we propose using this method to solve non-homogeneous fuzzy heat equation with triangular initial-boundary conditions. We examine the truncation error and the convergence conditions of the proposed method. Several numerical examples are presented to demonstrate the performance of the methods. The final results demonstrate the efficiency and the ability of the new fuzzy finite difference method to produce triangular fuzzy numerical results which are more consistent with existing reality.

Neville's and Romberg's processes: a fresh appraisal with extensions

1968 ◽  
Vol 263 (1144) ◽  
pp. 525-562 ◽  
Keyword(s):  
Power Series ◽  
Truncation Error ◽  
Point Of View ◽  
The Other ◽  
Matrix Formulation ◽  
Rounding Errors ◽  
Numerical Examples ◽  
Truncation Errors ◽  
Wide Range ◽  
Romberg Integration

In this paper Neville’s process for the repetitive linear combination of numerical estimates is re-examined and exhibited as a process for term-by-term elimination of error, expressed as a power series; this point of view immediately suggests a wide range of applications—other than interpolation, for which the process was originally developed, and which is barely mentioned in this paper—for example, to the evaluation of finite or infinite integrals in one or more variables, to the evaluation of sums, etc. A matrix formulation is also developed, suggesting further extensions, for example, to the evaluation of limits, derivatives, sums of series with alternating signs, and so on. It is seen also that Neville’s process may be readily applied in Romberg Integration; each suggests extensions of the other. Several numerical examples exhibit various applications, and are accompanied by comments on the behaviour of truncation and rounding errors as exhibited in each Neville tableau, to show how these provide evidence of progress in the improvement of the approximation, and internal numerical evidence of the nature of the truncation error. A fuller and more connected account of the behaviour of truncation errors and rounding errors is given in a later section, and suggestions are also made for choosing suitable specific original estimates, i.e. for choosing suitable tabular arguments in the elimination variable, in order to produce results as precise and accurate as possible.

scholarly journals On a linear interpolation problem for n-dimensional vector polynomials

2015 ◽  
Vol 199 ◽  
pp. 45-62 ◽  
Author(s):  
Mikhail Kudryavtsev ◽  
Sergio Palafox ◽  
Luis O. Silva
Keyword(s):  
Interpolation Problem ◽  
Linear Interpolation ◽  
Dimensional Vector

scholarly journals A Finite Difference Scheme for Compressible Miscible Displacement Flow in Porous Media on Grids with Local Refinement in Time

2013 ◽  
Vol 2013 ◽  
pp. 1-8
Author(s):  
Wei Liu
Keyword(s):  
Porous Media ◽  
Finite Difference ◽  
Linear Interpolation ◽  
Miscible Displacement ◽  
Flow In Porous Media ◽  
Finite Difference Schemes ◽  
Two Dimensional ◽  
Local Refinement ◽  
Numerical Examples ◽  
Compressible Miscible Displacement

Considering two-dimensional compressible miscible displacement flow in porous media, finite difference schemes on grids with local refinement in time are constructed and studied. The construction utilizes a modified upwind approximation and linear interpolation at the slave nodes. Error analysis is presented in the maximum norm and numerical examples illustrating the theory are given.

scholarly journals Approximation by generalized integral Favard-Szász type operators involving Sheffer polynomials

Filomat ◽  
2019 ◽  
Vol 33 (7) ◽  
pp. 1921-1935
Author(s):  
Seda Karateke ◽  
Çiğdem Atakut ◽  
İbrahim Büyükyazıcı
Keyword(s):  
Modulus Of Continuity ◽  
Order Of Convergence ◽  
Type Theorem ◽  
Type Operator ◽  
Weighted Spaces ◽  
Approximation Properties ◽  
Integral Type ◽  
Korovkin Type Theorem ◽  
Numerical Examples ◽  
Sheffer Polynomials

This article deals with the approximation properties of a generalization of an integral type operator in the sense of Favard-Sz?sz type operators including Sheffer polynomials with graphics plotted using Maple. We investigate the order of convergence, in terms of the first and the second order modulus of continuity, Peetre?s K-functional and give theorems on convergence in weighted spaces of functions by means of weighted Korovkin type theorem. At the end of the work, we give some numerical examples.

scholarly journals A New Three Step Iterative Method without Second Derivative for Solving Nonlinear Equations

2015 ◽  
Vol 12 (3) ◽  
pp. 632-637 ◽  
Author(s):  
Baghdad Science Journal
Keyword(s):  
Finite Difference Method ◽  
Iterative Method ◽  
Nonlinear Equations ◽  
Linear Interpolation ◽  
New Method ◽  
Second Derivative ◽  
Third Order ◽  
Numerical Examples ◽  
Newton Equation ◽  
Interpolation Analysis

In this paper , an efficient new procedure is proposed to modify third –order iterative method obtained by Rostom and Fuad [Saeed. R. K. and Khthr. F.W. New third –order iterative method for solving nonlinear equations. J. Appl. Sci .7(2011): 916-921] , using three steps based on Newton equation , finite difference method and linear interpolation. Analysis of convergence is given to show the efficiency and the performance of the new method for solving nonlinear equations. The efficiency of the new method is demonstrated by numerical examples.

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