查看更多>>摘要：In this paper, a system of time dependent boundary layer originated reaction dominated problems with diffusion parameters of different magnitudes, is considered for numerical analysis. The presence of these parameters lead to the boundary layer phenomena. Here, an optimal order uniformly accurate boundary layer adaptive method moving mesh method is proposed. This method is able to capture the layer phenomena without using a priori information of the solution. The problem is discretized by a modified implicit-Euler scheme in time direction. For the present system, adaptive mesh generation is required in space due to the singularly perturbed nature of the problem. For this purpose, a positive error monitor function is used whose equidistribution will move the mesh points towards the boundary layers. Parameter uniform error estimates are derived to show that the convergence rate is optimal with respect to the problem discretization. Numerical experiments strongly verify the theoretical findings and confirm the efficiency and accuracy of the proposed method. (C)& nbsp;2020 Elsevier B.V. All rights reserved.
查看更多>>摘要：This paper focuses on the numerical solutions of nonlinear delay-differential-algebraic equations with proportional delay, which are transformed into nonlinear delaydifferential-algebraic equation with constant delay through exponential transformation. Block boundary value methods are extended to solve this type of equation, and their unique solvability, convergence, and stability are rigorously proved, respectively. The computational effectiveness of the methods and correctness of the theoretical result are illustrated through numerical examples. (C) 2021 Elsevier B.V. All rights reserved.
查看更多>>摘要：This paper considers the pricing of equity-linked life insurance contracts with death and survival benefits in a general model with multiple stochastic risk factors: interest rate, equity, volatility, unsystematic and systematic mortality. We price the equity-linked contracts by assuming that the insurer hedges the risks to reduce the local variance of the net asset value process and requires a compensation for the non-hedgeable part of the liability in the form of an instantaneous standard deviation risk margin. The price can then be expressed as the solution of a system of non-linear partial differential equations. We reformulate the problem as a backward stochastic differential equation with jumps and solve it numerically by the use of efficient neural networks. Sensitivity analysis is performed with respect to initial parameters and an analysis of the accuracy of the approximation of the true price with our neural networks is provided. (C) 2021 Elsevier B.V. All rights reserved.
Castro-Martin, LuisRueda, Mara del MarFerri-Garcia, Ramon
8页
查看更多>>摘要：The convenience of online surveys has quickly increased their popularity for data collection. However, this method is often non-probabilistic as they usually rely on selfselection procedures and internet coverage. These problems produce biased samples. In order to mitigate this bias, some methods like Statistical Matching and Propensity Score Adjustment (PSA) have been proposed. Both of them use a probabilistic reference sample with some covariates in common with the convenience sample. Statistical Matching trains a machine learning model with the convenience sample which is then used to predict the target variable for the reference sample. These predicted values can be used to estimate population values. In PSA, both samples are used to train a model which estimates the propensity to participate in the convenience sample. Weights for the convenience sample are then calculated with those propensities. In this study, we propose methods to combine both techniques. The performance of each proposed method is tested by drawing nonprobability and probability samples from real datasets and using them to estimate population parameters. (C)& nbsp;2021 Elsevier B.V. All rights reserved.
查看更多>>摘要：In this paper, we study how to use Hessenberg-based methods to solve a class of complex matrix equations, which is a general form of many known equations. A generalized global Hessenberg process is presented to construct the basis of complex matrix space. This process requires less work and storage because the basis it uses has more zero components. Then global Hessenberg (Gl-Hess) and global CMRH (Gl-CMRH) methods are proposed, which can be directly realized by the original coefficient matrices. The convergence of the Gl-CMRH method is analyzed. Numerical experiments show the efficiency of the methods and compare them with existing methods. (C) 2021 Elsevier B.V. All rights reserved.
Behl, RamandeepBhalla, SoniaMagrenan, A. A.Kumar, Sanjeev...
16页
查看更多>>摘要：This study suggests a new general scheme of high convergence order for approximating the solutions of nonlinear systems. The proposed scheme is the extension of an earlier study of Parhi and Gupta. This method requires two vector-function, two Jacobian matrices, two inverse matrices, and one frozen inverse matrix per iteration. Convergence error, computational efficiency, and numerical experiments are performed to verify the applicability and validity of the proposed methods compared with existing methods. Finally, we discuss the strange fixed points and conjugacy functions on a particular case of our scheme. The basins of attractions also demonstrate the dynamical behavior of this special case in the neighborhood of required roots and also assert the theoretical outcomes. (C)& nbsp;2020 Elsevier B.V. All rights reserved.
查看更多>>摘要：Estimation of the stress-strength parameter, R = Pr(X < Y), is perhaps one of the challenging concepts in the reliability analysis. The estimation of R often criticized for its lack of stability and robustness against the presence of outliers and extreme values. The issue of estimating R under the presence of outliers is considered in this contribution for independently distributed random variables X and Y by the Pareto-based models. It is assumed that X has the Pareto distribution in the presence of outliers, whereas the random variable Y follows uncontaminated Pareto distribution. Under various assumptions on the parameters of the model, the maximum likelihood, method of moments, least squares, and modified maximum likelihood estimators are obtained. The shrinkage estimate of the stress-strength reliability parameter is also derived for each case using a prior guess, R-0. We conduct a Monte Carlo simulation study to compare the proposed methods of estimation. Finally, the performance of the postulated methodology is illustrated by analyzing two real-world datasets in the physical and insurance studies. (C) 2021 Elsevier B.V. All rights reserved.
查看更多>>摘要：We consider a mathematical model for skin contraction, which is based on solving a momentum balance under the assumptions of isotropy, homogeneity, Hooke's Law, infinitesimal strain theory and point forces exerted by cells. However, point forces, described by Dirac Delta distributions lead to a singular solution, which in many cases may cause trouble to finite element methods due to a low degree of regularity. Hence, we consider several alternatives to address point forces, that is, whether to treat the region covered by the cells that exert forces as part of the computational domain or as 'holes' in the computational domain. The formalisms develop into the immersed boundary approach and the 'hole' approach, respectively. Consistency between these approaches is verified in a theoretical setting, but also confirmed computationally. However, the 'hole' approach is much more expensive and complicated for its need of mesh adaptation in the case of migrating cells while it increases the numerical accuracy, which makes it hard to adapt to the multi-cell model. Therefore, for multiple cells, we consider the polygon that is used to approximate the boundary of cells that exert contractile forces. It is found that a low degree of polygons, in particular triangular or square shaped cell boundaries, already give acceptable results in engineering precision, so that it is suitable for the situation with a large amount of cells in the computational domain. (C) 2021 The Author(s). Published by Elsevier B.V.
查看更多>>摘要：We present a general truncated trust region method to solve large-scale nonlinear inverse problems. The truncated trust region method can serve as an implicit regularization method, and it can take advantage of the second-order derivative information of the misfit functional. The convergence of the truncated trust region method is provided under some smoothness assumptions. To improve the computational efficiency and reduce the memory requirement, we develop a second-order adjoint-state method to efficiently estimate matrix-vector products, and solve the trust region subproblem using the truncated conjugate gradient method with the matrix-free strategy. The full-waveform inversion problem is used to test the numerical performance of the proposed method. Numerical results show that the truncated trust region method can perform better than conventional methods (e.g. nonlinear conjugate gradient method and L-BFGS) for highly nonlinear inverse problems, in terms of inverting resolution. (C) 2021 Elsevier B.V. All rights reserved.
Cornejo, M. EugeniaDiaz-Moreno, Juan CarlosMedina, Jesus
18页
查看更多>>摘要：Usually, datasets contain imprecise data (noise), which can produce unsuspected results on the considered mappings. For instance, this can happen with the infimum and supremum operators, since both operators are straightforwardly associated with the universal and existencial quantifiers, respectively. An interesting possibility, of decreasing the impact of this possible noise in the final results, is the consideration of generalized quantifiers.& nbsp;This paper introduces four kinds of generalized quantifiers based on adjoint triples, which generalize the current approaches to a more flexible framework. Different properties and characterizations are studied and they have been applied to formal concept analysis, presenting the conjunctive and implicative concept-forming operators in this outstanding theory. (C) 2021 The Authors. Published by Elsevier B.V.
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