Numerical solution of Burgers' equation with high order splitting methods

Abstract In this work, high order splitting methods have been used for calculating the numerical solutions of Burgers' equation in one space dimension with periodic, Dirichlet, Neumann and Robin boundary conditions. However, splitting methods with real coefficients of order higher than two necessarily have negative coefficients and cannot be used for time-irreversible systems, such as Burgers' equations, due to the time-irreversibility of the Laplacian operator. Therefore, the splitting methods with complex coefficients and extrapolation methods with real and positive coefficients have been employed. If we consider the system as the perturbation of an exactly solvable problem (or one that can be easily approximated numerically), it is possible to employ highly efficient methods to approximate Burgers' equation. The numerical results show that both the methods with complex time steps having one set of coefficients real and positive, say ai ? ?+ and bi ? ?+, and high order extrapolation methods derived from a lower order splitting method produce very accurate solutions of Burgers' equation. © 2015 Published by Elsevier B.V

Effect of seed powder of a herbal legume fenugreek (Trigonella foenum-graceum L.) on growth performance, body components, digestive parts, and blood parameters of broiler chicks

The aim of this study was to investigate the effects of dietary Trigonella foenum-graceum L. seed powder (TFGSP) on growth performance, blood glucose, protein and lipid profile of broilers (Ross-308). One hundred ninety two, 1-d old mixed sex broiler chicks were allocated to 5 dietary treatments in which 0, 5, 10, 20 and 40 g TFGSP doses per kg commercial broiler diet were added for a period of 42 days. The results showed that body weight and the breast weight decreased after TFGSP treatment compared to control (P<0.05). Feed intake decreased after 5 g TFGSP treatment while 40 g TFGSP treatment decreased feed efficiency and leg weight compared to control (P<0.01). There was no significant difference in weights of digestive system parts, except duodenum weight and lipid oxidation between control and treatment groups. A 20 g TFGSP treatment enhanced blood glucose level (P<0.01), but decreased triglyceride level (P<0.01) compared to control. At 40 g TFGSP the blood cholesterol decreased (P<0.05) but LDL level increased compared to control (P<0.01). In conclusion, TFGSP addition to broiler diet decreased appetite and, consequently, reduced growth performance, more likely, attributting to the enhanced blood glucose level. Copyright 2013 Zoological Society of Pakistan