Showing papers in "Applied Mathematics and Computation in 1999"

TL;DR: A powerful modification of Adomian decomposition method is proposed that will accelerate the rapid convergence of the series solution and could lead to a promising approach for many applications in applied sciences.

TL;DR: Using the generalized hypergeometric function, a class of analytic functions with negative coefficients with coefficients estimates, distortion theorems, extreme points, and the radii of convexity and starlikeness are studied.

TL;DR: Taylor series methods for validated solutions of IVPs for ODEs are surveyed, several such methods in a common framework are described, and areas for future research are identified.

TL;DR: Using two-dimensional differential transform to solve Partial Differential Equations (PDE) is proposed in this study and three PDE problems with constant and variable coefficients are solved.

TL;DR: This study determined how to prepare an image for box-counting analysis, to define reasonable preferences for using the Fractal Dimension Calculator software, and to develop a routine procedure for defining the most appropriate range of box sizes for any one-piece image.

TL;DR: For Sturm-Liouville eigenvalue problems on time scales with separated boundary conditions, an oscillation theorem is given and Rayleigh's principle is established, new in the discrete case.

TL;DR: An analytic approximation for Volterra's model for population growth of a species in a closed system is presented and the Pade approximants are effectively used in the analysis to capture the essential behavior of the population u(t) of identical individuals.

TL;DR: A new approach to develop a nonperturbative approximate solution for the Thomas-Fermi equation rests on the recently developed modification of the Adomian decomposition method.

TL;DR: A mapping is introduced between the base graph Y, over which the sCA is defined and which represents the mutual dependencies of the local maps, and the update graph U, whose vertices are permutations of all Y-vertices, which represents a conceptual framework which allows to determine equivalence classes of sCA for a given graph X.

TL;DR: Hausdorff moment problem in the approach of maximum entropy is reconsidered and some aspects, as existence condition, entropy convergence, entropy decreasing, stability are studied through a unified approach.

TL;DR: In this article, sufficient conditions for the Cartesian product of two graphs to be maximum edge-connected, maximum point-connected (MPC), super edge-connectivity, super edge connected, or super point connected are presented.

TL;DR: It has been shown that the velocity of Love waves lies between two quantities which are dependent on the non-homogeneities of two media and when the medium is isotropic and the initial stress is absent, the dispersion equation obtained is in agreement with the corresponding results.

TL;DR: For given matrices A and E which are n matrices and matrices E, upper bounds for @?B^#@?, @?BB^#-A^##@?/@?A^ #@?

TL;DR: Numerical evidence is provided which suggests that regularization in combination with the most regular spectral filter for small values of the regularization parameter can provide good approximate solutions of the ill-posed Boussinesq equation for longer time than possible otherwise.

TL;DR: It is shown that for certain special cases, solutions of the equation can have chaotic behaviour through period doubling bifurcations.

TL;DR: A robust finite difference scheme for the integration of the Fokker-Planck (FP) equation with two variables plus time and the precision and stability of the scheme are verified.

TL;DR: The values of @l are characterized so that the boundary value problem has a positive solution and explicit intervals of@l are derived such that for any @l in the interval, existence of apositive solution of the boundaryvalue problem is guaranteed.

TL;DR: It is shown that populations of individual signal patterns in the central nervous system, may be adapted for maximum mean fitness in about the same manner as populations of organisms in the Darwinian evolution of natural systems.

TL;DR: The aim of the present paper is to investigate generation of waves in an orthotropic elastic solid medium under the influence of initial stress P and gravity field g and the frequency equation has been obtained.

TL;DR: This work develops a stopping criterion which is efficient for the computation of a regularized solution for the least-squares normal equations and can be suitably applied also to the Tikhonov regularization method.

TL;DR: A generalized AOR (GAOR) method is proposed here to solve the linear system with some special structure and the convergence result obtained here is an extension of the classical convergence result of the regular AOR method with weaker condition.

TL;DR: A new model is proposed for the (B,S)-market in which the stock price and the asset in the riskless bank account have hereditary price structures and the dynamics are described by linear stochastic functional differential equations.

TL;DR: The analysis is presented within the general framework of smoothing splines, of which interpolation is a special case, and the appropriate measure of roughness is defined in terms of the Fourier transform of g(|x|) be positive, except possibly at the origin.

TL;DR: Optimal convergence rates in H^1 and L^2 are demonstrated for this scheme and it is confirmed that larger time steps are appropriate with these scheme, and that the approximations exhibit improved qualitative behavior.

TL;DR: An index to measure the convexity of a convex function f at each point is defined and used to establish conditions on the convergence of the Halley method in the complex plane and in Banach spaces.

TL;DR: The detecting statistical method is an application of fuzzy classification and a generalization of Inclan and Tiao's result and an empirical application about change periods detecting for Taiwan monthly visitor's arrival is demonstrated.

TL;DR: Both regular and multiple scales asymptotic techniques are used for the analysis of the Euler forward difference method, and the resulting asymPTotic expansions are verified for several nonlinear, autonomous, ordinary differential equations.

TL;DR: The numerical tests show that this new algorithm converges faster than the previous norm-relaxed MFD for most test problems by selecting a set of suitable parameters even though it only has the same guaranteed convergence rate as the previous standard MFD.

TL;DR: The fixed point theory is used to investigate the existence and uniqueness of solutions of two-point boundary value problems (BVPs) for second order non-linear impulsive integro-differential equations on infinite intervals in a Banach space.

TL;DR: The predictability of the quasi-geostrophic ocean model is considered and the distribution of initial error with the fastest norm growth is distinguished, showing the initial data structure the most sensible to errors and points out the regions where the most accuracy should be required.