Related papers: Extended B-Spline Collocation Method For KdV-Burge…
Stable computational algorithms for the approximate solution of the Cauchy problem for nonstationary problems are based on implicit time approximations. Computational costs for boundary value problems for systems of coupled multidimensional…
This paper is devoted to the study of initial-boundary value problems for time-fractional analogues of Korteweg-de Vries, Benjamin-Bona-Mahony, Burgers, Rosenau, Camassa-Holm, Degasperis-Procesi, Ostrovsky and time-fractional modified…
This article focuses on the space-time isogeometric method for a linear time dependent fourth order problem. Using an auxiliary variable, first the problem is split into a system of two second order differential equations and then the…
We revisit the stochastic collocation method using the exponential of a quadratic spline. In particular, we look in details whether it is more appropriate to fix the ordinates and optimize the abscissae of an interpolating spline or to fix…
In this work we propose a novel approach to investigate boundary value problems (BVPs) for fully third order differential equations. It is based on the reduction of BVPs to operator equations for the nonlinear terms but not for the…
We develop two isogeometric divergence-conforming collocation schemes for incompressible flow. The first is based on the standard, velocity-pressure formulation of the Navier-Stokes equations, while the second is based on the rotational…
A scheme stemming from the use of pseudospectral approximations to spatial derivatives followed by a time integrator based on trigonometric polynomials is proposed for the numerical solutions of the coupled nonlinear Klein--Gordon…
For Kirchhoff plate bending problems on domains whose boundaries are curvilinear polygons a discretization method based on the consecutive solution of three second-order problems is presented. In Rafetseder and Zulehner (preprint,…
This paper investigates a boundary-value problem for the Korteweg-de Vries (KdV) equation on a star-graph structure. We develop a unified framework introducing the notion of $s$-compatibility, which generalizes classical compatibility…
We propose a new randomized method for solving systems of nonlinear equations, which can find sparse solutions or solutions under certain simple constraints. The scheme only takes gradients of component functions and uses Bregman…
This paper developed a method called "modified exponential cubic B-Spline differential quadrature (mExp-DQM) for space discretization together with a time integration algorithm" for the numerical computation of hyperbolic telegraph equation…
The space of $C^1$ cubic Clough-Tocher splines is a classical finite element approximation space over triangulations for solving partial differential equations. However, for such a space there is no B-spline basis available, which is a…
We propose a fast algorithm for the probabilistic solution of boundary value problems (BVPs), which are ordinary differential equations subject to boundary conditions. In contrast to previous work, we introduce a Gauss--Markov prior and…
This paper deals with balanced domain decomposition by constraints (BDDC) method for solving large-scale linear systems of algebraic equations arising from the space-time finite element discretization of parabolic initial-boundary value…
In this work, high order splitting methods have been used for calculating the numerical solutions of the Burgers' equation in one space dimension with periodic and Dirichlet boundary conditions. However, splitting methods with real…
Functions on a bounded domain in scientific computing are often approximated using piecewise polynomial approximations on meshes that adapt to the shape of the geometry. We study the problem of function approximation using splines on a…
The recent development of spectral method has been praised for its high-order convergence in simulating complex physical problems. The combination of embedded boundary method and spectral method becomes a mainstream way to tackle…
We develop the ultraspherical rectangular collocation (URC) method, a collocation implementation of the sparse ultraspherical method of Olver \& Townsend for two-point boundary-value problems. The URC method is provably convergent, the…
The paper focuses on pricing European-style options on several underlying assets under the Black-Scholes model represented by a nonstationary partial differential equation. The proposed method combines the Galerkin method with…
We prove the convergence of certain second-order numerical methods to weak solutions of the Navier-Stokes equations satisfying in addition the local energy inequality, and therefore suitable in the sense of Scheffer and…