Recently, there has been a growing interest in the production of electricity from renewable energy sources (RES). The RES investment is characterized by uncertainty, which is long-term, costly and depends on feed-in tariff and support schemes. In this paper, we address the real option valuation (ROV) of a solar power plant investment. The real option framework is investigated. This framework considers the renewable certificate price and, further, the cost of delay between establishing and operating the solar power plant. The optimal time of launching the project and assessing the value of the deferred option are discussed. The new three-stage numerical methods are constructed, the Lobatto3C-Milstein (L3CM) methods. The numerical methods are integrated with the concept of Black–Scholes option pricing theory and applied in option valuation for solar energy investment with uncertainty. The numerical results of the L3CM, finite difference and Monte Carlo methods are compared to show the efficiency of our methods. Our dataset refers to the Arab Republic of Egypt.

In this paper, we are interested in numerical methods with variable step-size for stochastic pantograph differential equations (SPDEs). SPDEs are very special stochastic delay differential equations (SDDEs) with unbounded memory. The problem of computer memory hold, when the numerical methods with constant step-size are applied to the SPDEs. In this work, we construct split-step theta (SSθ) methods with variable step-size for SPDEs. The boundedness and strong convergence of the numerical methods are investigated under a local Lipschitz condition and a coupled condition on the drift and diffusion coefficients. It is proved that, the SSθ methods with variable step-size for $\theta \in [\frac{1}{2},1]$ converge strongly to the exact solution. In addition, the strong order 0.5 is given under mild assumptions. The mean-square stability (MS-Stability) of the numerical methods with $\theta \in (\frac{1}{2},1]$ is given. Finally, some illustrative numerical examples are presented to show the efficiency of the methods, and how MS-Stability of SSθ methods depends on the parameter theta for both linear and nonlinear models.

The fundamental analysis of numerical methods for stochastic differential equations (SDEs) has been improved by constructing new split-step numerical methods. In this paper, we are interested in studying the mean-square (MS) stability of the new general drifting split-step theta Milstein (DSSθM) methods for SDEs. First, we consider scalar linear SDEs. The stability function of the DSSθM methods is investigated. Furthermore, the stability regions of the DSSθM methods are compared with those of test equation, and it is proved that the methods with θ≥3/2 are stochastically A-stable. Second, the nonlinear stability of DSSθM methods is studied. Under a coupled condition on the drifting and diffusion coefficients, it is proved that the methods with θ>1/2 can preserve the MS stability of the SDEs with no restriction on the step-size. Finally, numerical examples are given to examine the accuracy of the proposed methods under the stability conditions in approximation of SDEs.

In this paper, we discuss an EIQJR model with stochastic perturbation. First, a globally positive solution of the proposed model has been discussed. In addition, the global asymptotic stability and exponential mean-square stability of the disease-free equilibrium have been proven under suitable conditions for our model. This means that the disease will die over time. We investigate the asymptotic behavior around the endemic equilibrium of the deterministic model to show when the disease will prevail. Constructing a suitable Lyapunov functional method is crucial to our investigation. Parameter estimations and numerical simulations are performed to depict the transmission process of COVID-19 pandemic in China and to support analytical results.

The system of ordinary differential equations (ODEs) occurs in many fields of engineering science, particularly in the studies of electrical circuits, vibrations, chemical reactions and so on. In this paper we introduce analog cellular computing for solving ordinary differential equations (ODEs) based on cellular neural networks (CNNs) and study the stability. We apply the CNN to analyze and obtain the approximate solutions of the dynamics of (ODEs). The first system consists of two coupled of non-homogenous linear ordinary differential equations which is the Electrical network obtained from (Kirchhoff's Voltage Law) (Kreyszig, 2005). The second system consists of three coupled of non-homogenous nonlinear ordinary differential equations (Li et al., 2007). The computation based on CNN is advantageous as it provides accurate and ultra-fast solutions of ODEs.