Multilinear PageRank is a variant of the PageRank algorithm that takes into account multiple relationships among nodes in a network. This algorithm can make web page ranking more efficient and accurate by considering multiple types of connections …

Applying parallel-in-time algorithms to multiscale Hamiltonian systems to obtain stable long-time simulations is very challenging. In this paper, we present novel data-driven methods aimed at improving the standard parareal algorithm developed by …

In this paper, the conservation characteristic difference method based on the second-order modified upwind scheme is analyzed for solving the two-dimensional convection-diffusion equations by combining the splitting technique. Along each …

The aim of this study is to provide a rigorous description of a numerical approach based on the local min-orthogonal method for finding multiple eigenpairs of a quasilinear elliptic system. By a Rayleigh quotient formulation, the eigenvalue …

In this paper, we derive a new method to compute the nodes and weights of simultaneous n-point Gaussian quadrature rules. The method is based on the eigendecomposition of the banded lower Hessenberg matrix that contains the coefficients of the …

In this work, for solving large sparse vertical linear complementarity problems, a relaxation two-step modulus-based synchronous multisplitting method without auxiliary variable is constructed. The convergence conditions are presented for the …

For a high dimensional problem, a randomized Gram-Schmidt (RGS) algorithm is beneficial in computational costs as well as numerical stability. We apply this dimension reduction technique by random sketching to Krylov subspace methods, e.g. to the …

This paper presents adaptive, graded and uniform mesh schemes to approximate the solution of a fractional order advection-diffusion model, which generally shows a weak singularity at the initial time level. The temporal fractional derivative in …

Rational approximations of generalized hypergeometric functions $${}_pF_q$$ p F q of type $$(n+k,k)$$ ( n + k , k ) are constructed by the Drummond and factorial Levin-type sequence transformations. We derive recurrence relations for these …

The paper incorporates new methods of numerical linear algebra for the approximation of the biharmonic equation with potential, namely, numerical solution of the Dirichlet problem for $$ \left( \frac{d}{dx}\right) ^4u(x)+c(x)u(x)=\phi (x),\quad …

The present work is devoted to strong approximations of a generalized Aït-Sahalia model arising from mathematical finance. The numerical study of the considered model faces essential difficulties caused by a drift that blows up at the origin …

A spatial two-grid compact difference method for the nonlinear Volterra integro-differential equations with the Abel kernel is proposed to reduce the computational cost and improve the accuracy of the scheme. The proposed scheme firstly solves a …

A new approach for numerical solving initial value problems for systems of second-order nonlinear ordinary differential equations with a singularity of the first kind at the start point $$x=0$$ x = 0 is proposed. By substitution of the independent …

The Korpelevich method is an algorithm which is used to find solutions to equilibrium problems. These problems are mathematical models which are used in economics, game theory, and engineering. Pseudomonotone equilibrium problems are a specific …

In this paper, a generalized fuzzy barycentric Lagrange interpolation method is proposed to solve two-dimensional fuzzy fractional Volterra integral equations. Firstly, we use the generalized Gronwall inequality and iterative methods to …

This study focuses on the valuation of geometric Asian power options and presents an efficient numerical algorithm for solving the option price PDE. The analytical methodology utilizes the fractional Ito formula and replicating portfolio …

In this paper, we propose and analyze implicit residual-based a posteriori error estimates for the ultra-weak discontinuous Galerkin (UWDG) method for nonlinear second-order initial-value problems for ordinary differential equations of the form …

In the present paper, we consider the solution of periodic tridiagonal Toeplitz linear systems. By exploiting the special low-rank and Toeplitz structure, we give a new structure-preserving decomposition form of the coefficient matrix. Based on …

In this paper, we propose a multi-block relaxed-dual linear inertial alternating direction method of multipliers (MBRD-LIADMM) for solving the nonconvex and nonsmooth multi-block optimization problems with nonseparable structures, which combines …

In this paper, we propose a collocation scheme for efficiently solving the mixed time-fractional Black-Scholes (MTF-BS) model and obtaining the option price. Our approach involves deriving the mixed fractional Black-Scholes (MF-BS) partial …