In this paper, a symmetric Jacobi–Gauss collocation scheme is explored for both linear and nonlinear differential-algebraic equations (DAEs) of arbitrary index.After standard index reduction techniques, a type of Jacobi–Gauss collocation scheme with N knots is applied to differential part whereas another type of Jacobi–Gauss collocation scheme with N + 1 knots is applied to algebraic part of th...

Almost nothing decisive has been said about collocation methods for solving SPDEs. Among the best of such SPDEs the Burgers equation shows a prototypical model for describing the interaction between the reaction mechanism, convection effect, and diffusion transport. This paper discusses spectral collocation method to reduce stochastic Burgers equation to a system of stochastic ordinary differen...

We present Collocation Assistant, a prototype of a collocational aid designed to promote the collocational competence of learners of Japanese as a second language (JSL). Focusing on noun-verb constructions, the tool automatically flags possible collocation errors and suggests better collocations by using corrections extracted from a large annotated Japanese language learner corpus. Each suggest...

We develop and implement a collocation method to solve for an equilibrium in the dynamic legislative bargaining game of Duggan and Kalandrakis (2008). We formulate the collocation equations in a quasi-discrete version of the model, and we show that the collocation equations are locally Lipchitz continuous and directionally differentiable. In numerical experiments, we successfully implement a gl...

We develop an exponentially accurate fractional spectral collocation method for solving steady-state and time-dependent fractional PDEs (FPDEs). We first introduce a new family of interpolants, called fractional Lagrange interpolants, which satisfy the Kronecker delta property at collocation points. We perform such a construction following a spectral theory recently developed in [M. Zayernouri ...

Here we propose a new method based on projections for the approximate solution of eigenvalue problems. For an integral operator with a smooth kernel, using an interpolatory projection at Gauss points onto the space of (discontinuous) piecewise polynomials of degree ≤ r−1, we show that the proposed method exhibits an error of the order of 4r for eigenvalue approximation and of the order of 3r fo...

Spectral approximations for ODEs in unbounded domains have only received limited attention. In many applicable problems, singular initial value problems arise. In solving these problems, most of numerical methods have difficulties and often could not pass the singular point successfully. In this paper, we apply the sinc-collocation method for solving singular initial value problems. The ability...

. In this paper, we develop a quadratic spline collocation method for integrating the nonlinear partial differential equations (PDEs) of a plug flow reactor model. The method is proposed in order to be used for the operation of control design and/or numerical simulations. We first present the Crank-Nicolson method to temporally discretize the state variable. Then, we develop and analyze the pro...

‎The main purpose of this paper is to study the numerical solution of nonlinear Volterra integral equations with constant delays, based on the multistep collocation method. These methods for approximating the solution in each subinterval are obtained by fixed number of previous steps and fixed number of collocation points in current and next subintervals. Also, we analyze the convergence of the...