Numerical solution of the Schrodinger-Maxwell equations (with a general nonlinear term) via finite elements and genetic algorithms with Nelder-Mead

Authors:
Nikos E. Mastorakis
Affiliations:
WSEAS Research Department, Zografou, Athens, Greece and Technical University of Sofia, English Language Faculty, Industrial Engineering Department, Sofia, Bulgaria and Military Institutes of Unive ...
Venue:
FANDB'09 Proceedings of the 2nd WSEAS international conference on Finite differences, finite elements, finite volumes, boundary elements
Year:
2009

Citing 8
Cited 2

Unstable ordinary differential equations: solution via genetic algorithms and the method of Nelder-Mead

ISTASC'06 Proceedings of the 6th WSEAS International Conference on Systems Theory & Scientific Computation
The singular value decomposition (SVD) in tensors (multidimensional arrays) as an optimization problem. solution via genetic algorithms and method of Nelder-Mead

ISTASC'06 Proceedings of the 6th WSEAS International Conference on Systems Theory & Scientific Computation
The stability of collocation methods for approximate solution of singular integro-differential equations

WSEAS Transactions on Mathematics
Convergence of the collocation methods for singular integro-differential equations in Lebesgue spaces

WSEAS Transactions on Mathematics
Direct methods for numerical solution of singular integro-differential equations in classical Hölder spaces (case γ ≠ 0)

MACMESE'08 Proceedings of the 10th WSEAS international conference on Mathematical and computational methods in science and engineering
Genetic algorithms with Nelder-Mead optimization for the finite elements methods applied on non-linear problems in fluid mechanics

FANDB'09 Proceedings of the 2nd WSEAS international conference on Finite differences, finite elements, finite volumes, boundary elements
Genetic algorithms and Nelder-Mead method for the solution of boundary value problems with the collocation method

SMO'05 Proceedings of the 5th WSEAS international conference on Simulation, modelling and optimization
On the solution of ill-conditioned systems of linear and non-linear equations via genetic algorithms (GAs) and Nelder-Mead simplex search

EC'05 Proceedings of the 6th WSEAS international conference on Evolutionary computing

Existence, uniqueness and finite difference solution for the Dirichlet problem of the Schrodinger-Maxwell equations

WSEAS Transactions on Mathematics
Finite difference schemes for the Schrodinger-Maxwell equations (with a general non-linear term)

FANDB'09 Proceedings of the 2nd WSEAS international conference on Finite differences, finite elements, finite volumes, boundary elements

Quantified Score

Hi-index	0.00

Visualization

Abstract

Recently, the existence of a nontrivial solution to the nonlinear Schrodinger-Maxwell equations in R3, assuming on the nonlinearity the general hypotheses introduced by Berestycki & Lions has been proved. In this paper the Numerical Solution of the system of PDEs of Schrodinger-Maxwell equations (with a general nonlinear term) via Finite Elements and Genetic Algorithms with Nelder-Mead is proposed. The method of Finite Elements and Genetic Algorithms with Nelder-Mead that has been proposed by the author recently is also used.