zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
A shooting method for nonlinear heat transfer using automatic differentiation. (English) Zbl 1106.65064

Summary: The steady-state temperature distribution in a cylinder of unit radius is modeled by a nonlinear two-point boundary value problem with an endpoint singularity. We present a simple shooting method for the solution of this problem. It is well known that shooting methods solve initial-value problems repeatedly until the boundary conditions are satisfied. For the solution of the initial value problems, the method of this paper uses a technique known as automatic differentiation and obtains a Taylor series expansion for the solution.

Automatic differentiation is the process of obtaining the exact values of derivatives needed in the Taylor series expansion using recursive formulas derived from the governing differential equation itself. Thus, the method does not face the need to deal with step-size issues or the need to carry out lengthy algebraic manipulations for obtaining higher-order derivatives. The method successfully reproduces the solutions obtained by previous researchers.

MSC:
65L10Boundary value problems for ODE (numerical methods)
34B16Singular nonlinear boundary value problems for ODE