zbMATH — the first resource for mathematics

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.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
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)
The RKHSM for solving neutral functional-differential equations with proportional delays. (English) Zbl 1267.34133
Summary: We consider the following neutral functional-differential equations with proportional delays $$(u(t)+a(t)u(p_mt))^{(m)}=\beta u(t)+\sum\limits^{m-1}_{k=0}b_k(t)u^{(k)}(p_kt)+f(t),\quad t\geq 0,\tag{1}$$ with the initial conditions $$\sum\limits_{k=0}^{m-1}c_{ik}u^{(k)}(0)=\lambda_i,\quad i=0,1,\dotsc,m-1.\tag{2}$$ The reproducing kernel Hilbert space method (RKHSM) is applied to (1), (2). Its approximate solution is obtained by truncating the $n$-term of exact solution. Some examples are displayed to demonstrate the computation efficiency of the method. We also compare the performance of the method with a particular Runge-Kutta method, a one-leg $\theta $-method and variational iteration method. Experimental results indicate that the RKHSM is an accurate and efficient method for the solution of neutral functional-differential equations with proportional delays.

34K28Numerical approximation of solutions of functional-differential equations
34K06Linear functional-differential equations
Full Text: DOI