This chapter is dedicated to the numerical solution of a model Poisson equation, defined in a rectangular domain, with a known analytical solution. Five numerical methods are used for computing approximate solutions and comparing them with the known analytical solution. The first two methods, which ...
Saied. Numerical solution of the nonlinear Poisson-Boltzmann equation: Developing more robust and efficient methods. J. Comput. Chem., 16(3):337-364, 1995.Holst MJ, Saied F (1995) Numerical solution of the nonlinear Poisson-Boltzmann equation: developing more robust and ef- (R)cient methods....
little work has been done for solving Poisson's equation by using the Helmholtz decomposition scheme. To bridge this issue, we propose a novel efficient algorithm to solve Poisson's equation in irregular two dimensional domains for electrostatics through a quasi-Helmholtz decomposition techniqueu2014the...
A finite-difference method using a nonuniform triangle mesh is described for the numerical solution of the nonlinear two-dimen- sional Poisson equation Δ. (λΔα)+ s=0, where λ is a function of α or its derivatives, S is a function of position, and αor its normal derivative is ...
JournalofCommunicationandCompmer9(2012)977-980 DevelopmentofParallel ⋯ ⋯ NG AlgorithmforNumerical SolutionofThree--DimensionalPoissonEquation AlibekIssakhov DepartmentofMathematicalandComputerModeling,al—FarabiKazakhNationalUniversity,AImaty050040,Kazakhstan Received:May14,2012/Accepted:June15,2012/Published:...
The Poisson equation is solved using Numerov algorithm. The atom electron density is calculated by the self-consistent-field procedure. The final solution is obtained by the Richardson extrapolation. The RAtom program is presented, where all described algorithms are implemented. The RAtom is used ...
numericalapproximationofasinglesolutiontrajectoryandinsteadtoconsidera numericalmethodasadiscretedynamicalsystemwhichapproximatestheflowof thedifferentialequation–andsothegeometryofphasespacecomesbackagain throughthewindow.Thisviewallowsaclearunderstandingofthepreservationof invariantsandofmethodsonmanifolds,ofsymmetryandrev...
this paper, we consider numerical solution of the nonlinear Poisson-Boltzmann equation (PBE), the fundamental equation arising in the Debye-Huckel theory [1] of continuum molecular eletrostatics. In the case of a 1 : 1 electrolyte, this equation can be written as (#(r)#u(r)) + # (r)...
We consider the numerical solution of the Poisson-Boltzmann equation (PBE), a three-dimensional second order nonlinear elliptic partial di#erential equation arising in biophysics. This problem has several interesting features impacting numerical algorithms, including discontinuous coe#cients representing mater...
Efficient preconditioners for iterative solution of the boundary element equations for the three-dimensional Helmholtz equation 热度: symbolic derivation of finite difference approximations for the three-dimensional poisson equation 热度: A new phase-fitted modified Runge-Kutta pair for the numerical solution...