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)
Indexes and special discretization methods for linear partial differential algebraic equations. (English) Zbl 0941.65096

The authors consider linear partial differential algebraic equations with constant matrix coefficients of the form

Au t (t,x)+Bu xx (t,x)+Cu(t,x)=f(x,t)(1)

where A,B,CR n×n , at least one of the matrices A and B is singular and none of the matrices A or B is the zero matrix. The equation (1) is supplemented by the boundary (BCs) and initial conditions (ICs) at that, in general, any ICs and BCs cannot be prescribed for all components of the solution vector u(t,x).

Two numerical schemes by means of the method of lines and the scheme of the full discretization (BTCS) of initial boundary value problems for (1) are constructed. The influence of the differential spatial and the uniform differential time index on the convergence of the numerical solution to the exact solution is studied. Numerical examples using the BTCS scheme are presented.

MSC:
65M20Method of lines (IVP of PDE)
65M15Error bounds (IVP of PDE)
65M06Finite difference methods (IVP of PDE)
35R10Partial functional-differential equations
35K15Second order parabolic equations, initial value problems
65M12Stability and convergence of numerical methods (IVP of PDE)
Software:
MBSPACK