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A brief review of some application driven fast algorithms for elliptic partial differential equations

100%

Daripa P.

Open Mathematics

2012

tom 10

nr 1

204-216

Some application driven fast algorithms developed by the author and his collaborators for elliptic partial differential equations are briefly reviewed here. Subsequent use of the ideas behind development of these algorithms for further development of other algorithms some of which are currently in progress is briefly mentioned. Serial and parallel implementation of these algorithms and their applications to some pure and applied problems are also briefly reviewed.

Numerical investigation of a new class of waves in an open nonlinear heat-conducting medium

75%

Dimova M., Dimova S., Vasileva D.

Open Mathematics

2013

tom 11

nr 8

1375-1391

The paper contributes to the problem of finding all possible structures and waves, which may arise and preserve themselves in the open nonlinear medium, described by the mathematical model of heat structures. A new class of self-similar blow-up solutions of this model is constructed numerically and their stability is investigated. An effective and reliable numerical approach is developed and implemented for solving the nonlinear elliptic self-similar problem and the parabolic problem. This approach is consistent with the peculiarities of the problems - multiple solutions of the elliptic problem and blow-up solutions of the parabolic one.

Ograniczanie wyników

2 Open Mathematics

1 Daripa P.

1 Dimova M.

1 Dimova S.

1 Vasileva D.

1 2013

1 2012

Wyniki wyszukiwania

A brief review of some application driven fast algorithms for elliptic partial differential equations

Numerical investigation of a new class of waves in an open nonlinear heat-conducting medium