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Showing papers in "Applied Mathematics and Computation in 1990"


Journal ArticleDOI
TL;DR: In this article, the authors compare the properties of four explicit finite difference schemes used to integrate the nonlinear Klein-Gordon equation and find that the energy conserving scheme is the most suitable to study the long time behavior of the solutions.

121 citations


Journal ArticleDOI
TL;DR: In this article, the effect of small stochastic perturbations on systems that exhibit codimension-one and -two bifurcations is examined, and the asymptotic behavior of nonlinear dynamical systems in the presence of noise is studied using both the methods of Stochastic averaging and stochastically normal forms.

108 citations


Journal ArticleDOI
TL;DR: In this article, a new filled function, the globally convexized filled function (GFFL), is proposed, where the value tends to positive infinity as the norm of the variable vector tends to infinity, and it has no stationary point in the region in which the objective function value is greater than or equal to the least value found so far, but it does have a minimizer with a prefixed minimizer.

95 citations


Journal ArticleDOI
TL;DR: In this paper, continuous finite elements are used to develop numerical methods which preserve energy properties for nonlinear ordinary and partial differential equations, and time discretization algorithms for Cahn-Hilliard, Klein-Gordon, Korteweg-de Vries, and Schrodinger equations are presented.

51 citations


Journal ArticleDOI
TL;DR: In this paper, the dynamics of a population whose mathematical model is the equation of Verhulst is considered, and the moments and magnitudes of the impulses are determined so that the time of regeneration of the quantity of biomass taken away from the population be minimal.

47 citations


Journal ArticleDOI
TL;DR: In this paper, the Stokes equation is treated as a first order linear system, and a least squares method is used to minimize the defect in the differential operator in Sobolev spaces.

34 citations


Journal ArticleDOI
TL;DR: In this article, the authors examine the problem of cost allocation for the traveling-salesman problem (TSP) and note the significance of a "home" city for designing cost allocation schemes, focusing on TSPs with triangular inequality.

31 citations


Journal ArticleDOI
TL;DR: In this article, the density functions of T-invariant measures are constructed explicitly for an arbitrary piecewise linear transformation T: 0, 1]->[0, 1], where T is a constant.

30 citations


Journal ArticleDOI
TL;DR: Model-problem analysis or local-mode analysis is used to investigate the two-level convergence rates for multigrid Strokes solvers, finding that simple tranfer operators are sufficient to obtain optimal rates, but not in the anisotropic case.

30 citations


Journal ArticleDOI
TL;DR: In this article, a combination of interval derivative arithmetic and interval slope arithmetic can be used with the programming language Pascal-SC to obtain an enclosure of the range of a factorable function with @? @? C^2 (D) which is often narrower than that which is obtained by using slope arithmetic alone and which is always narrower than the one obtained by interval derivative algebra alone.

28 citations


Journal ArticleDOI
Bala Shetty1
TL;DR: In this paper, a heuristic algorithm for solving large scale capacitated facility location problems is presented, where the single source problem is solved by applying an iterative procedure in which lower bounds on the optimal objective value are generated through Lagrangian relaxation techniques.

Journal ArticleDOI
TL;DR: In this paper, the authors studied a periodic boundary value problem for a nonlinear ordinary differential equation of second order when the nonlinearity is given by a Caratheodory function and generalized the monotone iterative method to cover the fully nonlinear case.

Journal ArticleDOI
TL;DR: In this article, a technique for generating solution adaptive grids controlling cell volume is presented, where the grid control functions of the popular Poisson grid generators are defined to control cell size.

Journal ArticleDOI
TL;DR: In this article, random cellular automata were used to investigate the role of spatial factors in contagious disease. But, the authors did not consider the effect of the initial configuration of the infectives, and all other parameters remained fixed.

Journal ArticleDOI
TL;DR: In this paper, a general efficiency principle for stochastic population behavior is formulated and analyzed, which states that among all possible population states consistent with the same levels of activity, those states involving lower cost (or energy) expenditures are always at least as likely to occur as those states with higher expenditures.

Journal ArticleDOI
TL;DR: In this paper, a double Fourier series is developed to approximate the solutions of the convolution integral and Fredholm integral equations, and the operational matrix of integration together with the product operational matrix is utilized to reduce the computation of integral equations to a set of simultaneous linear algebraic equations.

Journal ArticleDOI
TL;DR: In this paper, a number of partial differential equations governing the dynamic behavior of different components of the hydrologic cycle in a region can be treated as abstract evolution equations in appropriate Hilbert spaces, when the source terms, the boundary conditions, the initial conditions, and/or the equation parameters are prescribed as stochastic processes.

Journal ArticleDOI
TL;DR: In this paper, a bound of 1 - O(k^(^@a^-^1^)^/^/@a) for a large number of levels k was derived for the multigrid F-cycle.

Journal ArticleDOI
TL;DR: In this paper, a simple mathematical model is constructed to determine the stability conditions of the biomass-carbon dioxide equilibrium of the atmosphere, which predicts that carbon dioxide emissions from fossil fuels in general will not disturb the equilibrium.

Journal ArticleDOI
TL;DR: In this paper, it was shown that an arbitrary scalar difference equation has a nontrivial invariant cone in the set of the nonnegative initial values if and only if the associated characteristic equation had a positive root.

Journal ArticleDOI
TL;DR: In this article, a method based on cell-mapping is proposed to locate all the roots of a nonlinear vector function, where the roots are asymptotically stable equilibrium points of the autonomous dynamical system and the domains of attraction associated with each root.

Journal ArticleDOI
TL;DR: Stochastic models of the subthreshold behavior of the membrane potential of neurons are considered and the problem of estimation of physiologically meaningful parameters of the developed models is considered.

Journal ArticleDOI
TL;DR: In this paper, a non-iterative transformation method for two-point boundary value problems with separated Dirichlet, Neumann, or DNeumann boundary conditions is defined, and the main feature of the method is the possibility of determining the numerical solution after two integrations.

Journal ArticleDOI
TL;DR: A mathematical model for the simulation of a localized measles epidemic is presented along with a computer simulation based on this model and the results are compared with the results of a measles outbreak which occured at Texas Tech University.

Journal ArticleDOI
TL;DR: This work uses the discrete version of the control-parametrization concept together with a simple constraint transcription to devise a computational algorithm for solving a class of constrained discrete-time optimal-control problems.

Journal ArticleDOI
TL;DR: The use of stochastic differential equations to aid in the analysis of problems in finance has been a hot topic in the last few decades as discussed by the authors, and the Black-Scholes formula for stock option prices, which is treated in this paper, is now used even by small town branches of brokerage firms.

Journal ArticleDOI
TL;DR: In this article, it was shown that the laws of motion expressed as differential equations governing the behavior of a system of particles break down when applied to the universe as a whole, due to the fact that the boundary conditions should in principle be reducible to particle interactions.

Journal ArticleDOI
TL;DR: A procedure for identifying approximate solutions to constrained optimization problems is described, using simple associative memories to map the inputs of closely related linear programs to optimal solution vectors.

Journal ArticleDOI
TL;DR: In this paper, an algorithm for the numerical computation of the Voigt line-broadening function V(x,y) is presented, which is expressed as an integral over [0,~] of a meromorphic function that invlove a free parameter.

Journal ArticleDOI
TL;DR: In this article, the stability of difference equations of Volterra type is discussed and a method of finding a linear equation equivalent to a given difference equation of VOLTERRA type is considered, and some stability properties of linear and nonlinear equations are investigated.