Computational and Applied Mathematics最新文献

The aim of this paper is to investigate a model of incompressible fluid of Bingham type in a bounded domain. We obtain the variational formulation of the model of incompressible fluid which is a variational–hemivariational inequality. The existence and uniqueness of the solution are proven utilizing recent advancements in the theory of hemivariational inequalities. Additionally, employing the finite element method, we analyze a fully discrete approximation of the model and provide error estimates for the approximate solutions. Finally, we demonstrate a continuous dependence result and establish the existence of optimal pairs for the incompressible fluid of Bingham type.

In literature, several tools have been developed to cope with ambiguity in data. Picture fuzzy set (PFS) is a very significant framework for extracting the maximum information from real-life phenomena with minimum uncertainty. Consequently, solving the muti-attribute decision-making (MADM) with the help of the PFS would be certainly useful. In this study, a short note on basic terms is provided for a better understanding of the article. A new class of operators picture fuzzy Schweizer–Sklar Maclaurin symmetric mean, picture fuzzy Schweizer–Sklar weighted Maclaurin Symmetric mean, picture fuzzy Schweizer–Sklar dual Maclaurin symmetric mean and picture fuzzy Schweizer–Sklar dual weighted Maclaurin symmetric mean is introduced. Some of the introduced AOs are applied to a real-life problem with the help of an illustrative example. For significance, the introduced AOs are compared to some existing AOs. The disparity of the results with the change in the involved parameters is also studied. The results obtained are tabulated and graphed.

In this article, we study the approximation properties of Durrmeyer-type sampling operators. We consider the composition of generalized sampling operators and Durrmeyer sampling operators. For the new composition operators, we provide the pointwise and uniform convergence, as well as the quantitative estimates in terms of the first-order modulus of continuity and K-functional. Moreover, we investigate the rate of convergence using weighted modulus of continuity. Also, difference estimates are provided for the operators. Additionally, we provide approximation results for the linear combinations of the composition operators. Finally, we discuss the rate of convergence for the operators via graphical example.

In this paper, by introducing an intermediate function, a splitting technique is employed for the fourth order time dependent non-linear Good Boussinesq equation. Then, an (H^{1})-Galerkin mixed finite element method is applied to the Good Boussinesq (GB) equation with cubic spline space as test and trial space in the method. This method may be considered as a Petrov-Galerkin method in which cubic splines are trial and linear splines (i.e second derivative of cubic splines)as test space. Optimal order error estimates are obtained for the both semi discrete scheme and fully discrete scheme. The Numerical illustration is presented to support the theoretical analysis.

The idea of nano-topology was originally proposed a decade ago by Thivagar. Since then, a lot of research has been done on the generalizations of the basic notions of nano-topology to overcome the limitations of an equivalence relation. The aim of this paper is to induce a novel frame of nano-topology using various covering-based neighborhoods via multiple ideals. The main properties of the proposed frame are acquired with the help of some illustrative instances, as well as its pros compared to the previous ones are investigated amply. A medical application is also discussed towards the end of this paper, where multi-ideal nano-topology is used to find the key symptoms of dengue disease. In addition, the most suitable medication is also suggested for the cure using the proposed theory.

The aim of this manuscript is to design and analyze a hybrid stable numerical algorithm for generalized fractional derivative (GFD) defined in Caputo sense (mathscr {D}^{alpha }_{0, Z,omega }) on non-uniform grid points in the temporal direction. An efficient and hybrid high order discretization is proposed for GFD by incorporating a ((3 - alpha ))-th order approximation using the moving refinement grid method for the initial interval in the temporal direction. The physical applications of the developed high order approximation are employed to design a hybrid numerical algorithm to determine the solution of the generalized time-fractional telegraph equation (GTFTE) and the generalized time-fractional stochastic telegraph equation (GTFSTE). The proposed numerical techniques are subjected to rigorous error analysis and a thorough investigation of theoretical results i.e. solvability, unconditional stability, convergence analysis, and comparative study are conducted with the existing scheme (Kumar et al. in Numer Methods Partial Differ Equ 35(3):1164–1183, 2019). Several test functions are utilized to verify that second-order convergence is attained in time which is higher than the order of convergence produced by the existing scheme (Kumar et al. 2019). In spatial direction, fourth-order convergence is obtained utilising the compact finite difference methods in spatial approximation on uniform meshes. A reduced first-order convergence in the temporal direction is reported for the GTFSTE model. Further, certain scaling and weight functions are used to show cast the impact of scaling and weight functions in the GFD.

Let G be a simple graph with vertex set (V(G),(|V(G)|=n)) and let (Ssubseteq V(G)). We denote by (d_{i}), the degree of the vertex (v_{i}). The graph (G^{S}) is obtained from G by removing all the vertices belonging to S (If (S={v_j}), then (G^S) is denoted by (G^{(j)})). The energy of G is the sum of all absolute values of the eigenvalues of the adjacency matrix A(G) and is denoted by ({mathcal {E}}(G)). Recently, Espinal and Rada (MATCH Commun Math Comput Chem 92(1):89–103, 2024) introduced the concept of local energy of a graph e(G). It is defined as (e(G)=sum ^n_{j=1},mathcal {E}_{G}(v _j)), where (mathcal {E}_{G}(v_j)=mathcal {E}(G)-mathcal {E}(G^{(j)})) is called the local energy of a graph G at vertex (v_j). In this paper, we prove that if (v_{1}in S) and S is a vertex independent set of size k such that every vertex in S share the same open neighborhood set (N_{G}(v_{1})), then (mathcal {E}(G)-mathcal {E}(G^{S})le 2,sqrt{k,d_{1}}). We also characterize graphs that satisfy the equality case. If (S={v_{1}}), we get (mathcal {E}(G)-mathcal {E}(G^{(1)})le 2,sqrt{d_{1}}) Espinal and Rada (MATCH Commun Math Comput Chem 92(1):89–103, 2024). One of the open problems in the study of local energy of a graph is to characterize graphs with (e(G)=2mathcal {E}(G)). Motivated by this problem, we present an infinite class of graphs for which (e(G)<2mathcal {E}(G)). As a result, we show that for a complete multipartite graph G, (e(G)=2mathcal {E}(G)) if and only if (Gcong K_{2}). We also prove that the local energy of a complete multipartite graph G is constant at each vertex of the graph if and only if G is regular. Finally, we give an upper bound on e(G) in terms of n and chromatic number k.

The main objective of this paper is to solve tensor absolute value equation when it has a positive solution. We derive several existence conditions for the positive solution of tensor absolute value equation with some structure tensors, and then propose a new fixed point iterative method for solving this class of equation. We study the convergence of the proposed method under appropriate conditions. Finally, we show the feasibility of the proposed method by three numerical examples.

In this paper, under the inclusion order, we focus on the investigations of fuzzy implications and coimplications on the poset of closed intervals of a given bounded poset. We first propose a method for constructing a fuzzy implication on the poset of closed intervals of a given bounded poset through the use of a fuzzy implication and a fuzzy coimplication on that given bounded poset. This process of constructing fuzzy implications is an extension of the fuzzy implication on that given bounded poset. We then explore some properties of this extended fuzzy implication and discuss about which properties of fuzzy implications are preserved in this extension. Moreover, we would like to apply the method of extending fuzzy implications for fuzzy coimplications. Although we present two methods for constructing fuzzy coimplications on the poset of closed intervals of a given bounded poset, these two methods are not the extension of the fuzzy coimplication on that given bounded poset. We also provide some illustrative examples.

In this work, we provide four methods for constructing new maximum sum-rank distance (MSRD) codes. The first method, a variant of cartesian products, allows faster decoding than known MSRD codes of the same parameters. The other three methods allow us to extend or modify existing MSRD codes in order to obtain new explicit MSRD codes for sets of matrix sizes (numbers of rows and columns in different blocks) that were not attainable by previous constructions. In this way, we show that MSRD codes exist (by giving explicit constructions) for new ranges of parameters, in particular with different numbers of rows and columns at different positions.