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This paper focuses on developing and analyzing a new AR-iterative scheme designed for estimating fixed points of generalized non-expansive mappings of the Suzuki kind. The scheme’s stability and convergence properties are rigorously proven, highlighting its superior convergence rate for non-expansive mappings when compared to existing schemes in the literature. Additionally, an application of the AR-iterative scheme to differential equations is presented. These findings underscore the effectiveness and versatility of the proposed scheme in numerical analysis and computational mathematics. [ABSTRACT FROM AUTHOR]

The aim of this paper is to introduce a novel approach for estimating the fixed points of multi-valued non-expansive mappings using the AR-iteration scheme in the context of uniformly convex Banach spaces. We establish strong and weak convergence results, providing rigorous analytical proofs and illustrating the results with a detailed example. Our approach showcases the potential of the AR-iteration scheme in solving real-world problems, particularly in addressing two-point boundary value problems. We demonstrate the applicability and effectiveness of the AR-iteration scheme in numerical analysis and computational mathematics. Our results contribute significantly to the advancement of numerical methods in solving boundary value problems, offering new insights and directions for future research in this area. Furthermore, we provide a detailed explanation of Green’s function approach and its implications for various scientific and engineering applications, paving the way for future research in this area. [ABSTRACT FROM AUTHOR]

In this paper-series, we investigate the performance of 12 explicit non-conventional algorithms. All of them have the convex combination property, thus they are unconditionally stable and preserve the positivity of the solution when they applied to the heat equation. In this part of the series, we construct several 2D systems to find how the errors depend on the time step size. Sweeps for other key parameters will be presented in the next part of the series. [ABSTRACT FROM AUTHOR]

This article explores about computational mathematics, which integrates numerical analysis, computer science, and mathematics to solve challenging scientific problems. To enable precise simulations, data analysis, optimisation, and mathematical modelling, computational mathematics makes use of cutting-edge algorithms, numerical techniques, and high-performance computing. In order to demonstrate the importance of computational mathematics for decision-making, scientific discovery, and engineering design, this study examines its key ideas, applications, and approaches. This article tries to demonstrate the transformative potential of computational mathematics in solving complicated issues and stimulating creativity by looking at real-world instances and developments, the use of algorithms, numerical analysis, mathematical modelling, and scientific computing in computational mathematics.

Generalized inverses of tensors play increasingly important roles in computational mathematics and numerical analysis. It is appropriate to develop the theory of generalized inverses of tensors within the algebraic structure of a ring. In this paper, we study different generalized inverses of tensors over a commutative ring and a noncommutative ring. Several numerical examples are provided in support of the theoretical results. We also propose algorithms for computing the inner inverses, the Moore–Penrose inverse, and weighted Moore–Penrose inverse of tensors over a noncommutative ring. The prowess of some of the results is demonstrated by applying these ideas to solve an image deblurring problem. [ABSTRACT FROM AUTHOR]

Dual Bernstein polynomials find many applications in approximation theory, computational mathematics, numerical analysis, and computer-aided geometric design. In this context, one of the main problems is fast and accurate evaluation both of these polynomials and their linear combinations. New simple recurrence relations of low order satisfied by dual Bernstein polynomials are given. In particular, a first-order non-homogeneous recurrence relation linking dual Bernstein and shifted Jacobi orthogonal polynomials has been obtained. When used properly, it allows to propose fast and numerically efficient algorithms for evaluating all n + 1 dual Bernstein polynomials of degree n with O(n) computational complexity. [ABSTRACT FROM AUTHOR]