Name
Abstract | ||
|---|---|---|
Standard explicit schemes for parabolic equations are not very convenient for computing practice due to the fact that they have strong restrictions on the time step. This stability restriction is avoided in some explicit schemes based on explicit-implicit splitting of the problem operator (Saul'yev asymmetric schemes, explicit alternating direction (ADE) schemes, group explicit method). These schemes are unconditionally stable, however, their approximation properties are worse than the usual implicit schemes. These explicit schemes are based on the so-called alternating triangle method and can be considered as factorized schemes in which the problem operator is split into a sum of two triangular operators that are adjoint to each other. Here we propose a multilevel modification of the alternating triangle method, which demonstrates better properties in terms of accuracy. We also consider explicit schemes of the alternating triangle method for the numerical solution of boundary value problems for systems of equations. The study is based on the general theory of stability (well-posedness) of operator-difference schemes. |
Year | DOI | Venue |
|---|---|---|
2014 | 10.1007/978-3-319-15585-2_18 | Lecture Notes in Computer Science |
Field | DocType | Volume |
Parabolic partial differential equation,Applied mathematics,Explicit method,Operator (computer programming),Mathematics | Conference | 8962 |
ISSN | Citations | PageRank |
0302-9743 | 0 | 0.34 |
References | Authors | |
2 | 2 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Petr N. Vabishchevich | 1 | 37 | 27.46 |
| Petr E. Zakharov | 2 | 0 | 0.34 |