Vol 31, No 3 (2023)

Solutions of many applied Cauchy problems for ordinary differential equations have one or more multiple zeros on the integration segment. Examples are the equations of special functions of mathematical physics. The presence of multiples of zeros significantly complicates the numerical calculation, since such problems are ill-conditioned. Round-off errors may corrupt all decimal digits of the solution. Therefore, multiple zeros should be treated as special points of the differential equations. In the present paper, a local solution transformation is proposed, which converts the multiple zero into a simple one. The calculation of the latter is not difficult. This makes it possible to dramatically improve the accuracy and reliability of the calculation. Illustrative examples have been carried out, which confirm the advantages of the proposed method.

The curvature tensor

Since the appearance of COVID-19, a huge amount of data has been obtained to help understand how the virus evolved and spread. The analysis of such data can provide new insights which are needed to control the progress of the epidemic and provide decision-makers with the tools to take effective measures to contain the epidemic and minimize the social consequences. Analysing the impact of medical treatments and socioeconomic factors on coronavirus transmission has been given considerable attention. In this work, we apply panel autoregressive distributed lag modelling (ARDL) to European Union data to identify COVID-19 transmission factors in Europe. Our analysis showed that non-medicinal measures were successful in reducing mortality, while strict isolation virus testing policies and protection mechanisms for the elderly have had a positive effect in containing the epidemic. Results of Dumitrescu-Hurlin paired-cause tests show that a bidirectional causal relationship exists for all EU countries causal relationship between new deaths and pharmacological interventions factors and that, on the other hand, some socioeconomic factors cause new deaths when the reverse is not true.