Nondominated sorting, also called Pareto Depth Analysis (PDA), is widely used in multi-objective optimization and has recently found important applications in multicriteria anomaly detection. Recently, a partial differential equation (PDE) continuum limit was discovered for nondominated sorting leading to a very fast approximate sorting algorithm called PDE -based ranking. We propose in this pa...

In this article, we study the numerical approximation of the solution of the Cauchy problem for a multidimensional linear parabolic PDE of second order, with unbounded time and space-dependent coefficients. The PDE free term and the initial data are also allowed to grow. Under the assumption that the PDE does not degenerate, using the L2 theory of solvability in weighted Sobolev spaces, the PDE...

This work concentrates upon the Mimetic discretization of elliptic partial differential equations (PDE). Numerical solutions are obtained and discussed for one-dimensional ODE on uniform and irregular grids and two-dimensional PDE on uniform grids. The focal point is to develop a scheme that incorporates the full tensor case on uniform grids in 2-D. The numerical results are then compared to pr...

We present high-order compact schemes for a linear second-order parabolic partial differential equation (PDE) with mixed second-order derivative terms in two spatial dimensions. The schemes are applied to option pricing PDE for a family of stochastic volatility models. We use a nonuniform grid with more grid-points around the strike price. The schemes are fourth-order accurate in space and seco...

PDE surfaces, whose behavior is governed by Partial Differential Equations (PDEs), have demonstrated many modeling advantages in surface blending, free-form surface modeling, and surface’s aesthetic or functional specifications. Although PDE surfaces can potentially unify geometric attributes and functional constraints for surface design, current PDE-based techniques exhibit certain difficultie...

We consider an image decomposition model involving a variational (minimization) problem and an evolutionary partial differential equation (PDE). We utilize a linear inhomogenuous diffusion constrained and weighted total variation (TV) scheme for image adaptive decomposition. An adaptive weight along with TV regularization splits a given image into three components representing the geometrical (...

In this study, we propose a secure communication scheme based on the synchronization of two identical fractional-order chaotic systems. The fractional-order derivative is in Caputo sense, and for synchronization, we use a robust sliding-mode control scheme. The designed sliding surface is taken simply due to using special technic for fractional-order systems. Also, unlike most manuscripts, the ...

A new method namely, denominator objective restriction method based on simplex method is proposed for solving linear fractional programming problems. Further, another method namely, decomposition-restriction method based on decomposition principle and the denominator objective restriction method is proposed for obtaining an optimal fuzzy solution to the fully fuzzy linear fractional programming...

We consider PDE/ODE systems for the simulation of intercellular signaling in multicellular environments. The intracellular processes for each cell described here by ODEs determine the long-time dynamics, but the PDE part dominates the solving effort. Thus, it is not clear if commonly used decoupling methods can outperform a coupling approach. Based on a sensitivity analysis, we present a system...