Growth of random errors in temperature forecasts by numerical method using centred time-differences

The growth of initial random errors in temperature forecasts by numerical method using centred time-differenced is investigated. Horizontal advection in one dimension is considered. Assuming that there is no correlation between the initial random errors as the different grid points and neglecting any correlation that may develop in the col1rse of computation, the random errors grow much more rapidly in this method than in forward time differencing. In both methods, correlations develop between the random errors at different grid points in the course of computation. When these are taken in to account, the growth of random errors is further enhanced in the forward differences. In the centred time-differences method, these correlations keep the random error almost at the initial level.

Damage of Solid Phase due to Explosion Effect Using Uzawa’s Algorithm

The paper deals with the impact of explosion on the damage development in the structure that forms a boundary of closed or semi-closed space – tunnel - the explosion in which is initiated. In the previous publications of the author the penalty formulation of the problem was used; now Uzawa’s algorithm is applied, which appears to be more promising algorithm accelerating the iterative process of damage development in the structure. Shock waves propagating in the airspace can be described by non-linear conservation equations starting with Euler’s equations which are used to be solved by forward differences of the system of pseudo-linear equations, using Arbitrary Lagrangian-Euler Method (ALE). Conservation equations are formulated for two phases: air and solid. In the solid phase, concrete lining, the time-dependent elasticity of free rectangular elements undergoing the damage, is solved by uniformly distributed boundary elements. The paper is focused on damage to the concrete lining due to impact of the explosion in the tunnel.

On Ostrowski and Gr"uss type discrete inequalities for second forward differences

The aim of the present article is to establish two new discrete Ostrowski and Gr"uss type inequalities involving functions and their first second forward differences.

A note on Ostrowski and Gr"uss type discrete inequalities

The aim of the present note is to establish some new discrete inequalities of the Ostrowski and Gr"uss type involving two functions and their forward differences.