Ferenc Szidarovszky

The Numerical Solution of Ordinary Differential Equations

In this chapter we shall study the following three central problems of the computational theory for ordinary differential equations: nProblem 1. Consider the ordinary differential equation n n

Systems Models for Mining Under Water Hazard

y(x), = f(x,y(x)),,y({x_0}), = ,{y_0},

Solution of Nonlinear Equations

n n(8.1) n n nwhere x is a scalar variable, and y and f are N-tuple-valued functions of the indicated variables. The problem of finding the function y(x) satisfying (8.1) for a given f and y 0 is called an initial-value problem. The solution of equation (8.1) has to be determined in an interval [x 0, b].

The Numerical Solution of Partial Differential Equations

Abstract Two methods are presented of estimating accumulated sediment yield stemming from erosion in a semiarid climate during a given time span, and the methods are compared from the viewpoint of the economic consequences evaluated within a Bayesian framework. The design of reservoirs requires the estimation of the random sediment volume Z accumulated over the lifetime of the project. An analytic and a simulation method are used to estimate the density function of Z and to calculate an economically optimal sediment storage space D*. A case study in Arizona, USA, is used to illustrate the methodology for the typical situation when only rainfall records are available. Both methods prove to be superior to the traditional procedure leaning on mean values. For the example considered, the two methods yield commensurate results. It appears that, in a semiarid basin, the effect of parameter uncertainty on both Z and D* may be considerably higher than that of natural uncertainty.

Approximation and Interpolation of Functions

Abstract Systems models for the following four elements of mining design under water hazard are shown: underground inflow forecasting, economic optimal design and reliability analysis of minewater control works, and regional multiobjective planning. Deep mining in a karstic aquifer is considered where mining - aquifer interaction is modeled on a regional scale by a deterministic finite difference scheme, and on a local scale by a stochastic forecasting method. Bayesian analysis, simulation, failure tree method of reliability estimation, dynamic programing, multiobjective decision-making are the basic tools for model solution. It is believed that modeling principles as shown can be used for other mining engineering purposes.

The Solution of Matrix Eigenvalue Problems

Simultaneous linear equations are equations of the form n n

General Theory for Iteration Methods

sumlimits_{j = 1}^n {{a_{ij}}{x_j}} , = ,{b_j},,1 leqslant i leqslant m,