Search results for "Numerical Analysis"

Multivariate exponential smoothing: A Bayesian forecast approach based on simulation

2009

This paper deals with the prediction of time series with correlated errors at each time point using a Bayesian forecast approach based on the multivariate Holt-Winters model. Assuming that each of the univariate time series comes from the univariate Holt-Winters model, all of them sharing a common structure, the multivariate Holt-Winters model can be formulated as a traditional multivariate regression model. This formulation facilitates obtaining the posterior distribution of the model parameters, which is not analytically tractable: simulation is needed. An acceptance sampling procedure is used in order to obtain a sample from this posterior distribution. Using Monte Carlo integration the …

Active macro-zone approach for incremental elastoplastic-contact analysis

2013

SUMMARY The symmetric boundary element method, based on the Galerkin hypotheses, has found an application in the nonlinear analysis of plasticity and in contact-detachment problems, but both dealt with separately. In this paper, we want to treat these complex phenomena together as a linear complementarity problem. A mixed variable multidomain approach is utilized in which the substructures are distinguished into macroelements, where elastic behavior is assumed, and bem-elements, where it is possible that plastic strains may occur. Elasticity equations are written for all the substructures, and regularity conditions in weighted (weak) form on the boundary sides and in the nodes (strong) betw…

Corrigendum to “Fractional differential equations solved by using Mellin transform” [Commun Nonlinear Sci Numer Simul 19(7) (2014) 2220–2227]

2015

An iterative method for pricing American options under jump-diffusion models

2011

We propose an iterative method for pricing American options under jump-diffusion models. A finite difference discretization is performed on the partial integro-differential equation, and the American option pricing problem is formulated as a linear complementarity problem (LCP). Jump-diffusion models include an integral term, which causes the resulting system to be dense. We propose an iteration to solve the LCPs efficiently and prove its convergence. Numerical examples with Kou@?s and Merton@?s jump-diffusion models show that the resulting iteration converges rapidly.

A numerical integration approach for fractional‐order viscoelastic analysis of hereditary‐aging structures

2019

Implicit analytic solutions for a nonlinear fractional partial differential beam equation

2020

Abstract Analytic solutions in implicit form are derived for a nonlinear partial differential equation (PDE) with fractional derivative elements, which can model the dynamics of a deterministically excited Euler-Bernoulli beam resting on a viscoelastic foundation. Specifically, the initial-boundary value problem for the corresponding PDE is reduced to an initial value problem for a nonlinear ordinary differential equation in a Hilbert space. Next, by employing the cosine and sine families of operators, a variation of parameters representation of the solution map is introduced. Due to the presence of a nonlinear term, a local fixed point theorem is employed to prove the local existence and u…

Order optimal preconditioners for fully implicit Runge-Kutta schemes applied to the bidomain equations

2010

The partial differential equation part of the bidomain equations is discretized in time with fully implicit Runge–Kutta methods, and the resulting block systems are preconditioned with a block diagonal preconditioner. By studying the time-stepping operator in the proper Sobolev spaces, we show that the preconditioned systems have bounded condition numbers given that the Runge–Kutta scheme is A-stable and irreducible with an invertible coefficient matrix. A new proof of order optimality of the preconditioners for the one-leg discretization in time of the bidomain equations is also presented. The theoretical results are verified by numerical experiments. Additionally, the concept of weakly po…

Controllability method for the Helmholtz equation with higher-order discretizations

2007

We consider a controllability technique for the numerical solution of the Helmholtz equation. The original time-harmonic equation is represented as an exact controllability problem for the time-dependent wave equation. This problem is then formulated as a least-squares optimization problem, which is solved by the conjugate gradient method. Such an approach was first suggested and developed in the 1990s by French researchers and we introduce some improvements to its practical realization. We use higher-order spectral elements for spatial discretization, which leads to high accuracy and lumped mass matrices. Higher-order approximation reduces the pollution effect associated with finite elemen…

Quasi-isometries associated to A-contractions

2014

Abstract Given two operators A and T ( A ≥ 0 , ‖ A ‖ = 1 ) on a Hilbert space H satisfying T ⁎ A T ≤ A , we study the maximum subspace of H which reduces M = A 1 / 2 T to a quasi-isometry, that is on which the equality M ⁎ M = M ⁎ 2 M 2 holds. In some cases, this subspace coincides with the maximum subspace which reduces M to a normal partial isometry, for example when A = T T ⁎ , and in particular if T ⁎ is a cohyponormal contraction. In this case the corresponding subspace can be completely described in terms of asymptotic limit of the contraction T. When M is quasinormal and M ⁎ M = A then the former above quoted subspace reduces to the kernel of A − A 2 . The case of an arbitrary contra…

Monotonic solution of heterogeneous anisotropic diffusion problems

2013

Anisotropic problems arise in various areas of science and engineering, for example groundwater transport and petroleum reservoir simulations. The pure diffusive anisotropic time-dependent transport problem is solved on a finite number of nodes, that are selected inside and on the boundary of the given domain, along with possible internal boundaries connecting some of the nodes. An unstructured triangular mesh, that attains the Generalized Anisotropic Delaunay condition for all the triangle sides, is automatically generated by properly connecting all the nodes, starting from an arbitrary initial one. The control volume of each node is the closed polygon given by the union of the midpoint of…