A very effective method for some kind of problems is the Method of Fundamental Solutions (MFS). It is a boundary meshless method which does not need any mesh and in linear problems only nodes (collocation points) on the domain boundaries and a set of source functions (fundamental solutions, i.e. Kelvin functions) in points outside the domain are necessary to satisfy the boundary conditions. Ano...

In this paper we show new solver strategies for the multigroup SPN equations for nuclear reactor analysis. By forming the complete matrix over space, moments, and energy, a robust set of solution strategies may be applied. Power iteration, shifted power iteration, Rayleigh quotient iteration, Arnoldi’s method, and a generalized Davidson method, each using algebraic and physics-based multigrid p...

In this paper the interval valued function is defined in the parametric form and its properties are studied. A methodology is developed to study the existence of the solution of a general interval optimization problem, which is expressed in terms of the interval valued functions. The methodology is applied to the interval valued convex quadratic programming problem.

Numerical computation of solutions for partial differential equations plays an important role in modern product development and engineering. Also, the use of computer aided design (CAD) software in the design process has become a widespread standard. These two fields are closely connected in the practical development process, but the corresponding techniques have been developed independently ov...

This paper addresses the problem of planning under uncertainty in large Markov Decision Processes (MDPs). Factored MDPs represent a complex state space using state variables and the transition model using a dynamic Bayesian network. This representation often allows an exponential reduction in the representation size of structured MDPs, but the complexity of exact solution algorithms for such MD...

Searching for objects in scenes is a natural task for people and has been extensively studied by psychologists. In this paper we examine this task from a connectionist perspective. Computational complexity arguments suggest that parallel feed-forward networks cannot perform this task efficiently. One difficulty is that, in order to distinguish the target from distractors, a combination of featu...

We consider the matrix equation AX + X⋆B = C , where the matrices A and B have sizes m × n and n × m, respectively, the size of the unknown X is n × m, and the operator (·)⋆ denotes either the transpose or the conjugate transpose of a matrix. In the first part of the paper, we review necessary and sufficient conditions for the existence and uniqueness of solutions. These conditions were obtaine...

A numerical procedure is presented for the efficient solution of sets of linearly coupled matrix Lyapunov equations. Such equations arise in numerical continuation methods for the design of robust and/or low-order control systems.

Integral and integro-differential equations are one of the most useful mathematical tools in both pure and applied mathematics. In this article, we present a variational iteration method for solving Fredholm integro-differential equations. This study provides an analytical approximation to determine the behavior of the solution. To show the efficiency of the present method for our proble...

This study concentrates on designing a medical waste management system with a hierarchical structure, including a local government and a waste management planner. The upper-level seeks to design and control the waste management facilities by minimizing the environmental risks related to the disposal of medical waste. While the lower-level model is to determine the waste collection plans by only...