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Abstract
Advantageous numerical methods for solving the Dirac equations are derived. They are based on different stochastic optimization techniques, namely the Genetic algorithms, the Particle Swarm Optimization and the Simulated Annealing method, their use of which is favored fromintuitive, practical, and theoretical arguments. Towards this end, we optimize appropriate parametric expressions representing the radial Dirac wave functions by employing methods that minimize multi parametric expressions in several physical applications. As a concrete application, we calculate the small (bottom) and large (top) components of the Dirac wave function for a bound muon orbiting around a very heavy (complex) nuclear system (the 208Pb nucleus), but the new approach may effectively be applied in other complex atomic, nuclear and molecular systems.
Program summary
Program Title: DiracSolver
Program Files doi: http://dx.doi.org/10.17632/7hv9mtdvmp.1
Licensing provisions: GPLv3
Programming language: GNUC++
Nature of problem: The software tackles the problem of solving the Dirac equation using stochastic optimization methods.
Solution method: The software utilizes three stochastic optimization methods for the solution of Dirac equation in the form of neural networks. The used methods are: genetic algorithm, particle swarm optimization and simulated annealing.
Program summary
Program Title: DiracSolver
Program Files doi: http://dx.doi.org/10.17632/7hv9mtdvmp.1
Licensing provisions: GPLv3
Programming language: GNUC++
Nature of problem: The software tackles the problem of solving the Dirac equation using stochastic optimization methods.
Solution method: The software utilizes three stochastic optimization methods for the solution of Dirac equation in the form of neural networks. The used methods are: genetic algorithm, particle swarm optimization and simulated annealing.
Original language  English 

Journal  Computer Physics Communications 
Volume  236 
Early online date  22 Oct 2018 
DOIs  
Publication status  Published  1 Mar 2019 
Keywords
 Neural networksGenetic algorithmSimulated annealingParticle swarm optimizationSolutions of the Dirac equations
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Dive into the research topics of 'DiracSolver: A tool for solving the Dirac equation'. Together they form a unique fingerprint.Projects
 1 Finished

Geometric Mechanics of Solids: new analysis of modern engineering materials  GEMS
Jivkov, A. (PI) & Margetts, L. (CoI)
1/11/16 → 31/10/21
Project: Research
Datasets

DiracSolver: A tool for solving the Dirac equation
Tsoulos, I. G. (Contributor), Kosmas, O. T. (Contributor) & Stavrou, V. N. (Contributor), Mendeley Data, 9 Nov 2018
DOI: 10.17632/7hv9mtdvmp.1, https://data.mendeley.com/datasets/7hv9mtdvmp
Dataset