# 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 family of variable mesh methods for the estimates of (d$u$/d$r$) and solution of non-linear two point boundary value problems with singularity. (English) Zbl 1071.65113
Summary: Using three grid points, we discuss variable mesh methods of order two and three for the numerical solution of the nonlinear differential equation ${u}^{\text{'}\text{'}}=f\left(r,u,{u}^{\text{'}}\right)$, $0 and the estimates of (d$u$/d$r$) subject to the natural boundary conditions $u\left(0\right)=A$ and $u\left(1\right)=B$. Both second- and third-order methods are compact and require two and three function evaluations, respectively. The proposed methods are successfully applied to the problems both in cartesian and polar coordinates. Numerical results are provided to illustrate the proposed methods and their convergence.
##### MSC:
 65L10 Boundary value problems for ODE (numerical methods) 65L50 Mesh generation and refinement (ODE) 34B15 Nonlinear boundary value problems for ODE 65L12 Finite difference methods for ODE (numerical methods) 65L20 Stability and convergence of numerical methods for ODE