Abstract:We consider initial value problems for the nonlinear Klein-Gordon equation in de Sitter spacetime. We use the differential transform method for the solution of the initial value problem. In order to show the accuracy of results for the solutions, we use the variational iteration method with Adomian's polynomials for the nonlinearity. We show that the methods are effective and useful.

In this paper, Wong-Zakai approximation methods are presented for some stochastic differential equations in engineering sciences. Wong-Zakai approximate solutions of the equations are analyzed and the numerical results are compared with results from popular approximation schemes for stochastic differential equations such as Euler-Maruyama and Milstein methods. Several differential equations from engineering problems containing stochastic noise are investigated as numerical examples. Results show that Wong-Zakai method is a reliable tool for studying stochastic differential equations and can be used as an alternative for the known approximation techniques for stochastic models.

Turbot (Psetta maxima) is a commercially valuable species in aquaculture, and the new strategies and models for growth are essential for rapid growth in aquaculture operations. Hence, the objectives of this study were to assess the best feeding protocol and growth model for turbot in culture conditions. Over a period of 2 years, growth data were recorded for the determination of the most suitable growth model. Starvation and subsequent refeeding were realized in juvenile fish. The fish were exposed to three feeding regimes. Control groups (C1 and C2) were fed daily to satiation throughout the weeks 11 and 14. Fish in the two treatments were deprived of food for 1‐week followed by 2 weeks or 1 week of refeeding (T1 and T2) in repeated cycles. In the second experimental group, fish were deprived of food for 1 day followed by 2 or 1 day of refeeding (T3 and T4) in repeated cycles. Length and weight were determined at daily/weekly feeding (C2/C1), feeding every other day/week (T4/T2), feeding at two‐day/week intervals (T3/T1) in all treatments. The results indicated that growth in the T1 and T4 groups exhibited similar results with the control group. Overall, alternative feeding strategies can be used instead of continuous feeding.

In this study, three Ito stochastic differential equations with multiplicative noise are investigated with Wong-Zakai method. The stochastic differential equations are also analyzed by Euler-Maruyama, Milstein and Runge Kutta stochastic approximation methods. The relative errors of these three methods are compared and the performance of Wong-Zakai method is shown alongside numerical results.