Temat: error bounds - Katalog OPAC zbiorów

Skocz do pozycji: 1.

Tytuł:: The finite difference approximation for the Dirichlet problem with a non-uniform mesh on a boundary
Autorzy:: Morawiec, Grażyna
Powiązania:: https://bibliotekanauki.pl/articles/747719.pdf
Data publikacji:: 1987
Wydawca:: Polskie Towarzystwo Matematyczne
Tematy:: Derivation of finite difference approximations
Error bounds
Opis:: .
The author describes a construction of the positive difference scheme, which is the approximation of the Dirichlet problem for an elliptic second order equation with mixed derivatives in an arbitrary region in R2. The a priori estimation for the approximate solution is proved and the estimation of the rate of convergence in maximum norm is established.
Źródło:: Mathematica Applicanda; 1987, 16, 30
1730-2668
2299-4009
Pojawia się w:: Mathematica Applicanda
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 2.

Tytuł:: Effective difference schemes for the heat equation in arbitrary regions
Autorzy:: Dryja, Maksymilian
Powiązania:: https://bibliotekanauki.pl/articles/748525.pdf
Data publikacji:: 1982
Wydawca:: Polskie Towarzystwo Matematyczne
Tematy:: Stability and convergence of difference methods,Error bounds
Opis:: .
In this paper the author considers the problem of the heat equation ∂u/∂t−(∂2u/∂x21+∂2u/∂x22)=f(x,t) for x∈Ω and t∈(0,T], u(x,0)=φ(x) for x∈Ω, u(x,t)=0 for x∈∂Ω and t∈[0,T]. He constructs a Crank-Nicolson and an alternating direction difference scheme on a regular mesh with steps hi (i=1,2) and τ. Linear interpolation is used for the approximation of the boundary condition. Besides stability of both schemes error estimates are derived under the condition that the derivatives ∂5u/∂t∂x4i and ∂3u/∂t3 are bounded. These estimates are: maxn∥un−yn∥A≤M(τ2+h3/2)andmaxn∥un−yn∥h≤M(τ2+h2+τh1/2+h5/2/τ). Here h=max(h1,h2), un=u(⋅,nτ), yn is the approximate value of un, ∥u∥2h=(u,u)h, (u,v)h=h1h2∑x∈Ωhu(x)v(x) (Ωh is the set of all mesh points lying in Ω), and ∥u∥2A=(u,Au)h where A is the discrete Laplace operator.
Źródło:: Mathematica Applicanda; 1982, 10, 19
1730-2668
2299-4009
Pojawia się w:: Mathematica Applicanda
Dostawca treści:: Biblioteka Nauki

Artykuł

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