Some algorithmic aspects of systems of PDEs based simulations can be better clarified by means of symbolic computation techniques. This is very important since numerical simulations heavily rely on solving systems of PDEs. For the large-scale problems we deal with in today’s standard applications, it is necessary to rely on iterative Krylov methods that are scalable (i.e., weakly dependent on t...

the present study introduces a new technique of homotopy perturbation method for the solution of systems of fractional partial differential equations. the proposed scheme is based on laplace transform and new homotopy perturbation methods. the fractional derivatives are considered in caputo sense. to illustrate the ability and reliability of the method some examples are provided. the results ob...

We consider an invariant skew-symmetric phase-space metric for nonHamiltonian systems. We say that the metric is an invariant if the metric tensor field is an integral of motion. We derive the time-dependent skewsymmetric phase-space metric that satisfies the Jacobi identity. The example of non-Hamiltonian systems with linear friction term is considered. PACS numbers: 45.20.−d, 02.40.Yy, 05.20.−y

Some algorithmic aspects of systems of PDEs based simulations can be better clarified by means of symbolic computation techniques. This is very important since numerical simulations heavily rely on solving systems of PDEs. For the large-scale problems we deal with in today’s standard applications, it is necessary to rely on iterative Krylov methods that are scalable (i.e., weakly dependent on t...

A model order reduction algorithm is derived, which is suitable for linear systems with a large number of inputs and outputs. The full system matrices may be non-symmetric, singular and do not require other properties like positive definiteness. Such systems typically arise from finite element discretization of partial differential equations describing coupled mechanical, electrical, acoustical...

We develop uniform approximations for the trace formula for non-integrable systems in which SU(2) symmetry is broken by a non-linear term of the Hamiltonian. As specific examples, we investigate Hénon-Heiles type potentials. Our formalism can also be applied to the breaking of SO(3) symmetry in a three-dimensional cavity with axially-symmetric quadrupole deformation. PACS number: 03.65.Sq