This paper is concerned with the numerical solutions of the vorticity transport equation (VTE) in two-dimensional space with homogenous Dirichlet boundary conditions. Namely, for this problem, the Crank-Nicolson finite difference equation is derived.  In addition, the consistency and stability of the Crank-Nicolson method are studied. Moreover, a numerical experiment is considered to study the convergence of the Crank-Nicolson scheme and to visualize the discrete graphs for the vorticity and stream functions. The analytical result shows that the proposed scheme is consistent, whereas the numerical results show that the solutions are stable with small space-steps and at any time levels.

In this study, a new technique is considered for solving linear fractional Volterra-Fredholm integro-differential equations (LFVFIDE's) with fractional derivative qualified in the Caputo sense. The method is established in three types of Lagrange polynomials (LP’s), Original Lagrange polynomial (OLP), Barycentric Lagrange polynomial (BLP), and Modified Lagrange polynomial (MLP). General Algorithm is suggested and examples are included to get the best effectiveness, and implementation of these types. Also, as special case fractional differential equation is taken to evaluate the validity of the proposed method. Finally, a comparison between the proposed method and other methods are taken to present the effectiveness of the proposal meth

Krawtchouk polynomials (KPs) and their moments are promising techniques for applications of information theory, coding theory, and signal processing. This is due to the special capabilities of KPs in feature extraction and classification processes. The main challenge in existing KPs recurrence algorithms is that of numerical errors, which occur during the computation of the coefficients in large polynomial sizes, particularly when the KP parameter (p) values deviate away from 0.5 to 0 and 1. To this end, this paper proposes a new recurrence relation in order to compute the coefficients of KPs in high orders. In particular, this paper discusses the development of a new algorithm and presents a new mathematical model for computing the

In this article, the high accuracy and effectiveness of forecasting global gold prices are verified using a hybrid machine learning algorithm incorporating an Adaptive Neuro-Fuzzy Inference System (ANFIS) model with Particle Swarm Optimization (PSO) and Gray Wolf Optimizer (GWO). The hybrid approach had successes that enabled it to be a good strategy for practical use. The ARIMA-ANFIS hybrid methodology was used to forecast global gold prices. The ARIMA model is implemented on real data, and then its nonlinear residuals are predicted by ANFIS, ANFIS-PSO, and ANFIS-GWO. The results indicate that hybrid models improve the accuracy of single ARIMA and ANFIS models in forecasting. Finally, a comparison was made between the hybrid foreca

In this research a new system identification algorithm is presented for obtaining an optimal set of mathematical models for system with perturbed coefficients, then this algorithm is applied practically by an “On Line System Identification Circuit”, based on real time speed response data of a permanent magnet DC motor. Such set of mathematical models represents the physical plant against all variation which may exist in its parameters, and forms a strong mathematical foundation for stability and performance analysis in control theory problems.

An Optimal Algorithm for HTML Page Building Process

Regression testing being expensive, requires optimization notion. Typically, the optimization of test cases results in selecting a reduced set or subset of test cases or prioritizing the test cases to detect potential faults at an earlier phase. Many former studies revealed the heuristic-dependent mechanism to attain optimality while reducing or prioritizing test cases. Nevertheless, those studies were deprived of systematic procedures to manage tied test cases issue. Moreover, evolutionary algorithms such as the genetic process often help in depleting test cases, together with a concurrent decrease in computational runtime. However, when examining the fault detection capacity along with other parameters, is required, the method falls sh

This paper proposes a novel meta-heuristic optimization algorithm called the fine-tuning meta-heuristic algorithm (FTMA) for solving global optimization problems. In this algorithm, the solutions are fine-tuned using the fundamental steps in meta-heuristic optimization, namely, exploration, exploitation, and randomization, in such a way that if one step improves the solution, then it is unnecessary to execute the remaining steps. The performance of the proposed FTMA has been compared with that of five other optimization algorithms over ten benchmark test functions. Nine of them are well-known and already exist in the literature, while the tenth one is proposed by the authors and introduced in this article. One test trial was shown t