Investigations of nonstandard, Mickens‐type, finite‐difference schemes for singular boundary value problems in cylindrical or spherical coordinates

By Ron Buckmire. 2003

66 citations recorded by the source corpus.

Subfields: Electrical and Electronic Engineering, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/09f4bb919a92e760c7994d788cef2a2571291f39

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In Electrical and Electronic Engineering

In Numerical Analysis

Citations in the corpus

APPLYING DIFFERENTIAL TRANSFORMATION METHOD TO THE ONE-DIMENSIONAL PLANAR BRATU PROBLEM (2007, background): “5) It was evaluated in [14], [11], [12] , [13] , [8] and [4] , that the critical value c λ is given by 513830719 .”
An algorithm based on the variational iteration technique for the Bratu-type and the Lane–Emden problems (2016, methodology): “The Bratu’s problem appears in a number of applications such as the fuel ignition model of the thermal combustion theory [7], chemical reaction theory and in the Chandrasekhar model of the expansion of the universe, radiative heat transfer and nano-technology [8–11].”
A Reliable Analytical Method for Solving Higher-Order Initial Value Problems (2013, methodology): “The Bratu model appears in a number of applications such as the fuel ignition of the thermal combustion theory, the model of the thermal reaction process, the Chandrasekhar model of the expansion of the universe, questions in geometry and relativity concerning the Chandrasekhar model, chemical react”
On the convergence of Mickens’ type nonstandard finite difference schemes on Lane-Emden type equations (2018, methodology): “In third section we have shown the convergence of the three schemes proposed in [4,5,16].”
Application of a Mickens finite‐difference scheme to the cylindrical Bratu‐Gelfand problem (2004, methodology): “In previous work ([4],[5],[6]) I have shown the usefulness of applying a particular Mickens-type finite-difference scheme to boundary value problems in cylindrical coordinates that contain the expression r du dr .”
On the use of nonstandard finite difference methods† (2005, background): “Buckmire [14] considered this problem with cylindrical radial operators, also known as the cylindrical Bratu-Gelfand problem.”
Nonstandard finite difference methods: recent trends and further developments (2016, methodology): “Some other relevant contributions falling under this categorywere use ofNSFD schemes to solve singular boundary value problems in cylindrical or spherical coordinates arising in theoretical aerodynamics (Buckmire [28]); limiting forms and associated mathematical properties of a nonlinear finite diff”