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This paper proposes an improved salp swarm algorithm (ISSA) as an effective metaheuristic method for tackling global optimization issues and damping power system oscillations. In the suggested ISSA, new equations are introduced to update the location of the leader and followers. This modification improves the method’s exploration possibilities while also preventing it from converging prematurely. Benchmark test functions are used to confirm the proposed algorithm’s performance, and the results are compared to SSA and other effective optimization algorithms. According to the extensive comparisons, the enhanced ISSA algorithm has higher convergence accuracy and stability than the original SSA and other researched algorithms. Furthermore, the feasibility and efficiency of the proposed method were demonstrated by the simultaneous coordinated design of UPFC based damping controllers. For the two-area, four-machine system, the experimental findings are provided. Simulation experiments reveal that ISSA designed controllers outperform those created using other methods.

We considered in this work the linear operator equation and used the Landweber iterative method as an iterative solver. After that, we used the multigrid method as an optimization method for obtaining an approximation solution with a highly accurate and fast process. A new parallel algorithm for the multigrid process has been developed. The proposed algorithm is based on a V-cycle mixed with the two-grid method. This modification of the V-cycle provides for parallel computing for each level. A coarse grid operator with a residual right-hand side vector for each coarse grid is provided. This parallel algorithm is used to accelerate and enhance computation for the solution of the iteration method in solving the inverse ill-posed problems. The necessary cost-time computation for all stages and processes for the parallel V-cycle algorithm has been done. A numerical experiment on solving the IVP (initial value problem) for the heat equation showed that the new parallel algorithm is much more efficient than the sequential method. • The study of iteration algorithms and mathematical experiments reveals a slow rate of convergence. • The Multigrid method is often used to speed up the rate of convergence of iterative methods, which is an effective method of solving large systems of linear algebra equations. • The approximation solution for the linear algebra equations was found by using the parallel method with the multigrid method.

The boundary value problem, BVP, for the PDE heat equation is studied and explained in this article. The problem declaration comprises two intervals; the (0, T) is the first interval and labels the heating of the inside burning chamber, and the second (T, ∞) interval defines the normal cooling of the chamber wall when the chamber temperature concurs with the ambient temperature. It is necessary to prove the boundary function of this problem has its place in the space H10,∞ in order to successfully apply the Fourier transform method. The applicability of the Fourier transform for time to this problem is verified. The method of projection regularization is used to solve the inverse boundary value problem for the heat equation and to obtain an evaluation for the error between the approximate and the real solution. These results are new and of practical interest as shown in the numerical case study.

The Landweber iteration method is one of the most popular methods for the solution of linear discrete ill-posed problems. The diversity of physical problems and the diversity of operators that result from them leads us to think about updating the main methods and algorithms to achieve the best results. We considered in this work the linear operator equation and the use of a new version of the Landweber iterative method as an iterative solver. The main goal of updating the Landweber iteration method is to make the iteration process fast and more accurate. We used a polar decomposition to achieve a symmetric positive definite operator instead of an identity operator in the classical Landweber method. We carried out the convergence and other necessary analyses to prove the usability of the new iteration method. The residual method was used as an analysis method to rate the convergence of the iteration. The modified iterative method was compared to the classical Landweber method. A numerical experiment illustrates the effectiveness of this method by applying it to solve the inverse boundary value problem of the heat equation (IBVP).

In this paper, the inverse problems for the boundary value and initial value in a heat equation are posed and solved. It is well known that those problems are ill posed. The problems are reformulated as integral equations of the first kind by using the separation-of-variables method. The discretization of the integral equation allowed us to reduce the integral equation to a system of linear algebraic equations or a linear operator equation of the first kind on Hilbert spaces. The Landweber-type iterative method was used in order to find an approximation solution. The V-cycle multigrid method is used to obtain more frequent and fast convergence for iteration. The numerical computation examples are presented to verify the accuracy and fast computing of the approximation solution.

Due to the huge amount of data obtained from students’ academic results in most tertiary institutions such as the colleges, polytechnics and universities, data mining has become one of the most effective tools for discovering vital knowledge from students’ dataset. The discovered knowledge can be productive in understanding numerous challenges in the scope of education and providing possible solutions to these challenges. The main objective of this research is to utilize the J48 decision algorithm model to test, classify and predict the students’ dataset by identifying some important attributes and instances. The analysis was conducted on the final year students’ academic results in C# programming amongst five universities which was imported in csv excel file dataset in WEKA environment. These training datasets contained the scores obtained in the examinations, grade remarks, grades, gender, and department. The knowledge extracted for the prediction model will help both the tutors and students to determine the success grade performance in the future. Flow lines, J48 decision trees, confusion matrices and a program flowchart were generated from the students’ dataset. The KAPPA value obtained from the prediction in this research ranges from 0.9070–0.9582 which perfectly agrees with the standard for an ideal analysis on datasets.