7,653 research outputs found
A unified approach for the solution of the Fokker-Planck equation
This paper explores the use of a discrete singular convolution algorithm as a
unified approach for numerical integration of the Fokker-Planck equation. The
unified features of the discrete singular convolution algorithm are discussed.
It is demonstrated that different implementations of the present algorithm,
such as global, local, Galerkin, collocation, and finite difference, can be
deduced from a single starting point. Three benchmark stochastic systems, the
repulsive Wong process, the Black-Scholes equation and a genuine nonlinear
model, are employed to illustrate the robustness and to test accuracy of the
present approach for the solution of the Fokker-Planck equation via a
time-dependent method. An additional example, the incompressible Euler
equation, is used to further validate the present approach for more difficult
problems. Numerical results indicate that the present unified approach is
robust and accurate for solving the Fokker-Planck equation.Comment: 19 page
Three real-space discretization techniques in electronic structure calculations
A characteristic feature of the state-of-the-art of real-space methods in
electronic structure calculations is the diversity of the techniques used in
the discretization of the relevant partial differential equations. In this
context, the main approaches include finite-difference methods, various types
of finite-elements and wavelets. This paper reports on the results of several
code development projects that approach problems related to the electronic
structure using these three different discretization methods. We review the
ideas behind these methods, give examples of their applications, and discuss
their similarities and differences.Comment: 39 pages, 10 figures, accepted to a special issue of "physica status
solidi (b) - basic solid state physics" devoted to the CECAM workshop "State
of the art developments and perspectives of real-space electronic structure
techniques in condensed matter and molecular physics". v2: Minor stylistic
and typographical changes, partly inspired by referee comment
Un método Wavelet-Galerkin para ecuaciones diferenciales parciales parabólicas
In this paper an Adaptive Wavelet-Galerkin method for the solution ofparabolic partial differential equations modeling physical problems withdifferent spatial and temporal scales is developed. A semi-implicit timedifference scheme is applied andB-spline multiresolution structure on theinterval is used. As in many cases these solutions are known to presentlocalized sharp gradients, local error estimators are designed and an ef-ficient adaptive strategy to choose the appropriate scale for each time isdeveloped. Finally, experiments were performed to illustrate the applica-bility and efficiency of the proposed method.En este trabajo se desarrolla un método Wavelet-Galerkin Adaptativopara la resolución de ecuaciones diferenciales parabólicas que modelanproblemas físicos, con diferentes escalas en el espacio y en el tiempo. Seutiliza un esquema semi-implícito en diferencias temporales y la estructuramultirresolución de las B-splines sobre intervalo.Como es sabido que enmuchos casos las soluciones presentan gradientes localmente altos, se handiseñado estimadores locales de error y una estrategia adaptativa eficientepara elegir la escala apropiada en cada tiempo. Finalmente, se realizaronexperimentos que ilustran la aplicabilidad y la eficiencia del método pro-puestoFil: Vampa, Victoria Cristina. Universidad Nacional de La Plata. Facultad de Ingeniería; ArgentinaFil: Martín, María Teresa. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de La Plata. Facultad de Ingeniería; Argentin
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