Métodos numéricos para resolução de equações diferenciais ordinárias lineares baseados em interpolação por spline

In this work we have elaborated a spline-based method of solution of inicial value problems involving ordinary differential equations, with emphasis on linear equations. The method can be seen as an alternative for the traditional solvers such as Runge-Kutta, and avoids root calculations in the linear time invariant case. The method is then applied on a central problem of control theory, namely, the step response problem for linear EDOs with possibly varying coefficients, where root calculations do not apply. We have implemented an efficient algorithm which uses exclusively matrix-vector operations. The working interval (till the settling time) was determined through a calculation of the least stable mode using a modified power method. Several variants of the method have been compared by simulation. For general linear problems with fine grid, the proposed method compares favorably with the Euler method. In the time invariant case, where the alternative is root calculation, we have indications that the proposed method is competitive for equations of sifficiently high order.

Detecção de metamidofós em solos por métodos ecotoxicológico e cromatografia líquida acoplada à espectrometria de massas sequencial (LC-MS/MS)

Soil contamination by pesticides is an environmental problem that needs to be monitored and avoided. However, the lack of fast, accurate and low cost analytical methods for discovering residual pesticide in complex matrices, such as soil, is a problem still unresolved. This problem needs to be solved before we are able to assess the quality of environmental samples. The intensive use of pesticides has increased since the 60s, because the dependence of their use, causing biological imbalances and promoting resistance and recurrence of high populations of pests and pathogens (upwelling). This has contributed to the appearance of new pests that were previously under natural control. To develop analytical methods that are able to quantify residues pesticide in complex environment. It is still a challenge for many laboratories. The integration of two analytical methods one ecotoxicological and another chemical demonstrates the potential for environmental analysis of methamidophos. The aim of this study was to evaluate an ecotoxicological method as "screening" analytical methamidophos in the soil and perform analytical confirmation in the samples of the concentration of the analyte by chemical method LC-MS/MS In this work we tested two soils: a clayey and sandy, both in contact with the kinetic methamidophos model followed pseudo-second order. The clay soil showed higher absorption of methamidophos and followed the Freundlich model, while the sandy, the Langmuir model. The chemical method was validated LC-MS/MS satisfactory, showing all parameters of linearity, range, precision, accuracy, and sensitivity adequate. In chronic ecotoxicological tests with C. dubia, the NOEC was 4.93 and 3.24 for ng L-1 of methamidophos to elutriate assays of sandy and clay soils, respectively. The method for ecotoxicological levels was more sensitive than LC-MS/MS detection of methamidophos, loamy and sandy soils. However, decreasing the concentration of the standard for analytical methamidophos and adjusting for the validation conditions chemical acquires a limit of quantification (LOQ) in ng L-1, consistent with the provisions of ecotoxicological test. The methods described should be used as an analytical tool for methamidophos in soil, and the ecotoxicological analysis can be used as a "screening" and LC-MS/MS as confirmatory analysis of the analyte molecule, confirming the objectives of this work