Tau and Galerkin Operational Matrices of Derivatives for Treating Singular and Emden-Fowler Third-order Type Equations

2021 ◽  
Author(s):  
W. M. Abd-Elhameed ◽  
H. M. Ahmed
Keyword(s):  
Order Type ◽  
Operational Matrices ◽  
Third Order

A clock steering method: using a third-order type 3 DPLL equivalent to a Kalman filter with a delay

Metrologia ◽  
2015 ◽  
Vol 52 (6) ◽  
pp. 864-877
Author(s):  
Yiwei Wu ◽  
Hang Gong ◽  
Xiangwei Zhu ◽  
Gang Ou
Keyword(s):  
Kalman Filter ◽  
Order Type ◽  
Third Order ◽  
Type 3

scholarly journals Some Algorithms for Solving Third-Order Boundary Value Problems Using Novel Operational Matrices of Generalized Jacobi Polynomials

2015 ◽  
Vol 2015 ◽  
pp. 1-10 ◽  
Author(s):  
W. M. Abd-Elhameed
Keyword(s):  
Boundary Value Problems ◽  
Jacobi Polynomials ◽  
Boundary Value ◽  
Operational Matrix ◽  
Operational Matrices ◽  
Algebraic Equations ◽  
Third Order ◽  
Generalized Jacobi Polynomials ◽  
Nonlinear Algebraic Equations ◽  
Derivatives Of

The main aim of this research article is to develop two new algorithms for handling linear and nonlinear third-order boundary value problems. For this purpose, a novel operational matrix of derivatives of certain nonsymmetric generalized Jacobi polynomials is established. The suggested algorithms are built on utilizing the Galerkin and collocation spectral methods. Moreover, the principle idea behind these algorithms is based on converting the boundary value problems governed by their boundary conditions into systems of linear or nonlinear algebraic equations which can be efficiently solved by suitable solvers. We support our algorithms by a careful investigation of the convergence analysis of the suggested nonsymmetric generalized Jacobi expansion. Some illustrative examples are given for the sake of indicating the high accuracy and efficiency of the two proposed algorithms.

scholarly journals Towards an integrated stratigraphy of the Gramame Formation (Maastrichtian), CIPASA quarry, Pernambuco-Paraíba Basin, NE Brazil

2006 ◽  
Vol 29 (1) ◽  
pp. 81-94
Author(s):  
Francisco Henrique de Oliveira Lima ◽  
Eduardo A. M Koutsoukos
Keyword(s):  
Order Type ◽  
Passive Margin ◽  
Northeastern Brazil ◽  
Calcareous Nannofossils ◽  
Calcareous Nannofossil ◽  
Warm Climate ◽  
Third Order ◽  
Transgressive System Tract ◽  
System Tract ◽  
Integrated Stratigraphy

This study presents the integrated biostratigraphic (calcareous nannofossils and foraminifera), petrographic, geochemical and ichnological analyzes of the Gramame Formation (Maastrichtian) at the CIPASA Quarry section, in the Pernambuco-Paraíba Basin, northeastern Brazil. A high resolution calcareous nannofossil biostratigraphic study has been carried out, allowing to subdivide the studied section into three subzones of Maastrichtian age: CC25A, CC25B, and CC25C. Each biostratigraphic unit was further characterized by petrographic, geochemical and ichnological parameters. During the Maastrichtian the area was characterized by a dry and warm climate with low influx of terrigenous sediments. These conditions were fundamental to the widespread development of a carbonate ramp system in an outer neritic to bathyal setting, with deposition of alternating calcareous mudstones and argillaceous mudstones of the Gramame Formation. The Gramame Formation belongs to the transgressive system tract of second-order type, characteristic of a Passive Margin Sequence. The studied section consists of part of a third order deposicional cycle, which is arranged in a transgressive systems tract and a highstand systems tract. The lowstand systems tract was not characterized.

Solutions of the Blasius and MHD Falkner-Skan boundary-layer equations by modified rational Bernoulli functions

2017 ◽  
Vol 27 (8) ◽  
pp. 1687-1705 ◽  
Author(s):  
Velinda Calvert ◽  
Mohsen Razzaghi
Keyword(s):  
Boundary Layer ◽  
Rational Functions ◽  
Operational Matrices ◽  
Algebraic Equations ◽  
Nonlinear Boundary Value Problems ◽  
Infinite Domain ◽  
Third Order ◽  
Content Type ◽  
Boundary Layer Equations ◽  
Bernoulli Functions

Purpose This paper aims to propose a new numerical method for the solution of the Blasius and magnetohydrodynamic (MHD) Falkner-Skan boundary-layer equations. The Blasius and MHD Falkner-Skan equations are third-order nonlinear boundary value problems on the semi-infinite domain. Design/methodology/approach The approach is based upon modified rational Bernoulli functions. The operational matrices of derivative and product of modified rational Bernoulli functions are presented. These matrices together with the collocation method are then utilized to reduce the solution of the Blasius and MHD Falkner-Skan boundary-layer equations to the solution of a system of algebraic equations. Findings The method is computationally very attractive and gives very accurate results. Originality/value Many problems in science and engineering are set in unbounded domains. One approach to solve these problems is based on rational functions. In this work, a new rational function is used to find solutions of the Blasius and MHD Falkner-Skan boundary-layer equations.

scholarly journals Harmonic balance analysis of pull-in range and oscillatory behavior of third-order type 2 analog PLLs

2020 ◽  
Vol 53 (2) ◽  
pp. 6378-6383
Author(s):  
N.V. Kuznetsov ◽  
M.Y. Lobachev ◽  
M.V. Yuldashev ◽  
R.V. Yuldashev ◽  
G. Kolumbán
Keyword(s):  
Harmonic Balance ◽  
Order Type ◽  
Oscillatory Behavior ◽  
Third Order ◽  
Harmonic Balance Analysis ◽  
Balance Analysis
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