Narrow Results

In this research, we conducted an analysis using a stochastic neural network (SNN) approach to explore the dynamics of Ebola virus disease. Ebola virus, commonly referred to as Ebola hemorrhagic fever, is initially transmitted to humans through contact with wild and domesticated animals. Subsequently, it spreads rapidly among individuals through person-to-person transmission. To control the spread of the Ebola virus, we employed a five-compartmental mathematical model comprising the following classes: susceptible ($S$), exposed ($E$), infected ($I$), quarantined ($Q$) and recovered ($R$). We utilized the aforementioned SNN method for this purpose. The primary aim of this study is two-fold: first, to assess the convergence and accuracy of our proposed method, and second, to elucidate the impact of Ebola disease control measures. Lastly, we conducted a comparative analysis of our findings with those obtained from the numerical solvers ode15s and ode23e, demonstrating the precision and efficacy of our technique in addressing the current disease challenge.

Coupled first order IVPs are frequently used in many parts of engineering and sciences. In this article, we presented a code including three computer programs which are joint with the Matlab software to solve and plot the solutions of the first order coupled stiff or non-stiff IVPs. Some engineering and scientific problems related to IVPs are given and fuel depletion (production of the ²³⁹Pu isotope) in a Pressurized Water Nuclear Reactor (PWR) are computed by the present code.

In this paper, we modify the Runge–Kutta–Fehlberg code of fourth and fifth order with the purpose of solving initial value problems established on ordinary differential equations involving complex-valued functions of one complex variable, which are allowed to have high complexity in their definition, when integration along prescribed complex paths is required. Such initial value problems arise in certain astrophysical issues, like the polytropic models, applied to polytropic stars, and the general-relativistic polytropic models, applied to neutron stars. Comparison with similar codes is made by applying to these models.

Given a right-continuous Markov process (X_t)_{t ≥ 0} on a second countable metrizable space E with transition semigroup (p_t)_{t ≥ 0}, we prove that there exists a σ-finite Borel measure μ with full support on E, and a closed and densely defined linear operator generating (p_t)_{t ≥ 0} on L^p (E; μ). In particular, we solve the corresponding Cauchy problem in L^p (E; μ) for any initial condition . Furthermore, for any real β > 0 we show that there exists a generalized Dirichlet form which is associated to (e^-βt p_t)_{t ≥ 0}. If the β-subprocess of (X_t)_{t ≥ 0} corresponding to (e^-βt p_t)_{t ≥ 0}, β > 0, is μ-special standard then all results from generalized Dirichlet form theory become available, and Fukushima's decomposition holds for . If (X_t)_{t ≥ 0} is transient, then β can be chosen to be zero.

Perturbation–Iteration algorithms (PIA) have been developed recently to solve differential equations analytically. A continuous solution in terms of closed form functions as an approximation of the original equation can be found using the method. The method has been implemented to algebraic equations, ordinary and partial differential equations successfully. Based on the formalism developed previously, in this work, purely numerical versions of the perturbation–iteration algorithms are proposed for the first time for first-order nonlinear ordinary differential equations. The new algorithms are called as the Numerical Perturbation–Iteration Algorithms (NPIA) to distinguish them from the continuous analytical ones (PIA) and the method in general will be called the Numerical Perturbation–Iteration Method (NPIM). Iteration schemes based on one correction term in the perturbation solution and first-order derivatives in the Taylor series expansions (NPIA(1,1)), and one correction term in the perturbations and second-order derivatives in the series expansions (NPIA(1,2)) are derived. The numerical results are compared with the exact solutions and a very good match is observed. NPIA(1,2) produced slightly better results compared to NPIA(1,1) with total errors being at least $O(h^2)$, $h$ being the step size for both methods. An improvement suggestion for NPIA(1,1) is proposed in the last section to eliminate unrealistic blow-up solutions which are encountered for some specific equations.

We discuss the existence of weak solutions with moving phase boundaries in thermoelasticity related to dynamic phase transitions. One of the goals is to study the dynamical consequence of the stable and metastable states defined in this paper. We use the entropy condition and the kinetic relation as the main admissibility criteria to study the above goals for the Euler equations with nonmonotone constitutive relation. We discuss the case where there are two noninteracting phase boundaries moving in the opposite directions. A modification to treat the case where the two phase boundaries collide is also discussed.

The main difficulty in solving nonlinear differential equations by the differential transformation method (DTM) is how to treat complex nonlinear terms. This method can be easily applied to simple nonlinearities, e.g. polynomials, however obstacles exist for treating complex nonlinearities. In the latter case, a technique has been recently proposed to overcome this difficulty, which is based on obtaining a differential equation satisfied by this nonlinear term and then applying the DTM to this obtained differential equation. Accordingly, if a differential equation has n-nonlinear terms, then this technique must be separately repeated for each nonlinear term, i.e. n-times, consequently a system of n-recursive relations is required. This significantly increases the computational budget. We instead propose a general symbolic formula to treat any analytic nonlinearity. The new formula can be easily applied when compared with the only other available technique. We also show that this formula has the same mathematical structure as the Adomian polynomials but with constants instead of variable components. Several nonlinear ordinary differential equations are solved to demonstrate the reliability and efficiency of the improved DTM method, which increases its applicability.

In this paper, we consider tumor-immune interaction model systems. The numerical solutions for the tumor-immune interaction system are obtained by using the 2-point Block Backward Differentiation Formula (BBDF) methods developed by Zarina et al. in 2007. The numerical results are presented in terms of computational time and accuracy of the solutions.

In this short article, we investigate the controllability of damped second-order initial value problems for a class of differential inclusions with nonlocal conditions on unbounded real interval. We shall employ a theorem of Ma¹, which is an extension to multivalued maps on locally convex topological spaces, of Schaefer's theorem. Example is provided to illustrate the theory. This work is motivated by the papers of Benchohra and Ntouyas² and Benchohra, Gatsori and Ntouyas³.

Consider initial value problems of type

This paper formulates sufficient conditions on the real-valued coefficients of the operator having the form