Computational and Mathematical Methods最新文献

Solving stiff, singular, and singularly perturbed initial value problems (IVPs) has always been challenging for researchers working in different fields of science and engineering. In this research work, an attempt is made to devise a family of nonlinear methods among which second- to fourth-order methods are not only $��𝒜�-�$ stable but $��𝒜�-�$ acceptable as well under order stars' conditions. These features make them more suitable for solving stiff and singular systems in ordinary differential equations. Methods with remaining orders are either zero- or conditionally stable. The theoretical analysis contains local truncation error, consistency, and order of accuracy of the proposed nonlinear methods. Furthermore, both fixed and variable stepsize approaches are introduced wherein the latter improves the performance of the devised methods. The applicability of the methods for solving the system of IVPs is also described. When used to solve problems from physical and real-life applications, including nonlinear logistic growth and stiff model for flame propagation, the proposed methods are found to have good results.

An analysis of stagnation point flow of heat and mass transfer of double diffusive mixed-convective stream with radiating vertical plate and convective boundary conditions. The Runge–Kutta method with shooting procedure is used to solve the transformed equations mathematically. An accuracy of the numerical procedure has been validated through a restriction of the current work compared with prior available results. The shear surface stress, Nusselt and Sherwood number are increased with increase in Prandtl number. The Biot number $��\mathrm{Bi}�>�0.1�$ is investigated and observed that to increase the Prandtl number, the friction coefficient, Nusselt number and Sherwood number are increased. The impact of pertinent constraints on distinct flow parameters are determined and analyzed through tables and graphs.

The aim of this article is to show a way in which the problem of predicting the evolution of an epidemic may be tackled by describing it in the framework of Boltzmann's kinetic theory, as it has been developed and applied in the last years to complex systems by a suitable modification of the Boltzmann equation, via a suitable reinterpretation of state variables and the introduction of the notion of «functional subsystems». Accordingly, in this article we model an arbitrary (national) population S as a complex system, split in two functional subsystems, the first containing all single individuals of S and the second containing the «care tools», that are to be meant as available places in hospitals with a sufficient number of physicians and of equipments for intensive cares. The state variable on the first subsystem will be the «health state», and the state variable on the other will be the «effectiveness». We shall then write a system of nonlinear ordinary differential equations which gives the evolution of the probability distribution on the set of possible values of the health states. By assigning data partly on the basis of plausibility assumptions and partly as estimated from those furnished by institutions of Campania region, the system takes a form allowing the numerical simulation of such evolution, which will be performed and presented in a forthcoming paper.

Dam safety is a relevant aspect in our society due to the importance of its functions (power generation, water supply, lamination of floods) and due to the potentially catastrophic consequences of a serious breakdown or breakage. Dam safety analyses are fundamentally based on behavior models, which are idealizations of the dam-foundation that allow us to calculate the dam's response to a certain combination of actions. The comparison of this response with the real one, measured by the auscultation or survey devices, is the main element to determine the safety status of the structure. To improve this analysis, it is necessary to increase the accuracy of the numerical models obtaining a digital twin that allows knowing, in a faithful way, how the structure is going to work in normal and extreme situations.

In this work, we present an original block preconditioner to improve the convergence of Krylov solvers for the simulation of two-phase flow in porous media. In our modeling approach, the set of coupled governing equations is addressed in a fully implicit fashion, where Darcy's law and mass conservation are discretized in an original way by combining the mixed hybrid finite element (MHFE) and the finite volume (FV) methods. The solution to the sequence of large-size nonsymmetric linearized systems of equations that stem during a full-transient simulation represents the most time and resource consuming task, thus motivating the need for efficient preconditioned Krylov solvers. The proposed preconditioner exploits the block structure of the Jacobian matrix while coping with the nonsymmetric nature of the individual blocks. Both academic and realistic applications have been used to challenge the preconditioner, allowing to point out its robustness, stability and overall computational efficiency.

Big data mining is related to large-scale data analysis and faces computational cost-related challenges due to the exponential growth of digital technologies. Classical data mining algorithms suffer from computational deficiency, memory utilization, resource optimization, scale-up, and speed-up related challenges in big data mining. Sampling is one of the most effective data reduction techniques that reduces the computational cost, improves scalability and computational speed with high efficiency for any data mining algorithm in single and multiple machine execution environments. This study suggested a Euclidean distance-based stratum method for stratum creation and a stratified random sampling-based big data mining model using the K-Means clustering (SSK-Means) algorithm in a single machine execution environment. The performance of the SSK-Means algorithm has achieved better cluster quality, speed-up, scale-up, and memory utilization against the random sampling-based K-Means and classical K-Means algorithms using silhouette coefficient, Davies Bouldin index, Calinski Harabasz index, execution time, and speedup ratio internal measures.

In this article we propose an implementation, for irregular cloud of points, of the meshless method called generalized finite difference method to solve the fully nonlinear Eikonal equation in 2D and 3D. We obtain the explicit formulas for derivatives and solve the system of nonlinear equations using the Newton–Raphson method to obtain the approximate numerical values of the function for the discretization of the domain. It is also shown that the approximation of the scheme used is of second order. Finally, we provide several examples of its application over irregular domains in order to test accuracy of the scheme, as well as comparison with order numerical methods.

Higher order compact scheme (HOC) is used for pricing both European and American type passport option. We consider the problem for two different cases, namely, the symmetric case (which has a closed form solution) and the non-symmetric case. For the symmetric case HOC schemes result in slightly improved results as compared to the classical Crank–Nicolson implicit method, while still giving approximately second order convergence rate. In order to improve the convergence rate, grid stretching near zero accumulated wealth is introduced in the HOC schemes. The consequent higher order compact scheme with grid stretching gives better results with the rate of convergence being close to third order. For non-symmetric case we also observe similar results for both European and American type passport option. In absence of any analytic formula for the non-symmetric case, convergence rate was calculated using double-mesh differences.

In this article, we presented an asymptotic SDFEM for singularly perturbed convection diffusion type differential difference equations with point source term. First, the solution is decomposed into two functions, among them one is the solution of delay differential equation and other one is the solution of differential equation with point source. Furthermore, using the asymptotic expansion approximation, the delay differential equation is modified as a nondelay differential equations. Streamline diffusion finite element methods are applied to approximate the solutions of the two problems. We prove that the present method gives an almost second-order convergence in maximum norm and square integrable norm, whereas first-order convergence in $��{�H�}^{�1�}�$ norm. Numerical results are presented to validate the theoretical results.