Journal•ISSN: 1818-9962
Lobachevskii Journal of Mathematics
Springer Science+Business Media
About: Lobachevskii Journal of Mathematics is an academic journal published by Springer Science+Business Media. The journal publishes majorly in the area(s): Boundary value problem & Computer science. It has an ISSN identifier of 1818-9962. Over the lifetime, 2187 publications have been published receiving 6548 citations. The journal is also known as: LJM.
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TL;DR: The paper presents AMGCL -- an opensource C++ library implementing the algebraic multigrid method (AMG) for solution of large sparse linear systems of equations, usually arising from discretization of partial differential equations on an unstructured grid.
Abstract: The paper presents AMGCL—an opensource C++ library implementing the algebraic multigrid method (AMG) for solution of large sparse linear systems of equations, usually arising from discretization of partial differential equations on an unstructured grid. The library supports both shared and distributed memory computation, allows to utilize modern massively parallel processors via OpenMP, OpenCL, or CUDA technologies, has minimal dependencies, and is easily extensible. The design principles behind AMGCL are discussed and it is shown that the code performance is on par with alternative implementations.
67 citations
TL;DR: The concept of (α, β)-fuzzy interior ideal in ordered semigroups is introduced, which is a generalization of a fuzzy interior idealin ordered semigroup.
Abstract: In this paper, we introduce the concept of (α, β)-fuzzy interior ideal in ordered semigroups, which is a generalization of a fuzzy interior ideal in ordered semigroup. We investigate the related properties of ordered semigroups in terms of (α, β)-fuzzy interior ideals. The concepts of an (∈,∈ ∨q)-fuzzy interior ideal and (∈,∈ ∨q)-fuzzy ideal coincide in case of regular(resp. intra-regular) ordered semigroups.
62 citations
TL;DR: In this article, the double Laplace and double Sumudu transforms were used to solve the wave equation in one dimension having singularity at initial conditions, and they produced some properties and relationship between them.
Abstract: In this paper, we produce some properties and relationship between double Laplace and double Sumudu transforms. Further, we use the double Sumudu transform to solve wave equation in one dimension having singularity at initial conditions.
59 citations
Journal Article•
51 citations
TL;DR: In this paper, the authors discuss the classical statement of group classification problem and some extensions in the general case, and carry out the complete extended group classification for a class of (1 + 1)-dimensional nonlinear diffusion-convection equations with coefficients depending on the space variable.
Abstract: We discuss the classical statement of group classification problem and some its extensions in the general case. After that, we carry out the complete extended group classification for a class of (1 + 1)-dimensional nonlinear diffusion-convection equations with coefficients depending on the space variable. At first, we construct the usual equivalence group and the extended one including transformations which are nonlocal with respect to arbitrary elements. The extended equivalence group has interesting structure since it contains a non-trivial subgroup of non-local gauge equivalence transformations. The complete group classification of the class under consideration is carried out with respect to the extended equivalence group and with respect to the set of all point transformations. Usage of extended equivalence and correct choice of gauges of arbitrary elements play the major role for simple and clear formulation of the final results. The set of admissible transformations of this class is preliminary investigated.
50 citations