in this paper, the chebyshev spectral collocation method(cscm) for one-dimensional linear hyperbolic telegraph equation is presented. chebyshev spectral collocation method have become very useful in providing highly accurate solutions to partial differential equations. a straightforward implementation of these methods involves the use of spectral differentiation matrices. firstly, we transform ...

The well-known explicit linear multistep methods for the numerical solution of ordinary differential equations advance the numerical solution from xn+k_x to xn+k ky comPut'ng some numerical approximation from back values and then evaluating the problem defining function to obtain an approximation of the derivative. In this paper similar methods are proposed that first compute an approximation t...

It is well known that a necessary condition for the Lax-stability of the method of lines is that the eigenvalues of the spatial discretization operator, scaled by the time step k, lie within a distance O(k) of the stability region of the time integration formula as k ~ O. In this paper we show that a necessary and sufficient condition for stability, except for an algebraic factor, is that the e...

We derive a manifestly gauge invariant low energy blocked action for Yang-Mills theory using operator cutoff regularization, a prescription which renders the theory finite with a regulating smearing function constructed for the proper-time integration. By embedding the momentum cutoff scales in the smearing function, operator cutoff formalism allows for a direct application of Wilson-Kadanoff r...

Across-the-space parallelism still remains the most mature, convenient and natural way to parallelize large scale problems. One of the major problems here is that implicit time stepping is often difficult to parallelize due to the structure of the system. Approximate implicit schemes have been suggested to circumvent the problem [5]. These schemes have attractive stability properties and they a...

This paper investigates the expected benefits of the implicit time integration scheme in the solution of jointed rock problems. Discontinuous Deformation Analyses (DDA) exploits the unconditional stability of the implicit time integration scheme, and allows the time step size of the solution to be much larger than the critical time step size dictated by the stability requirement of the explicit...

Article history: Received 31 August 2012 Accepted 26 January 2013 Available online 8 February 2013

A general class of convergent methods for the numerical solution of ordinary differential equations is employed to obtain a class of convergent generalized reducible quadrature methods for Volterra integral equations of the second kind and Volterra integro-differential equations.

This paper contains error estimates for covolume discretizations of Maxwell’s equations in three space dimensions. Several estimates are proved. First, an estimate for a semi-discrete scheme is given. Second, the estimate is extended to cover the classical interlaced time marching technique. Third, some of our unstructured mesh results are specialized to rectangular meshes, both uniform and non...

Inspired by recent advances in the theory of modified differential equations, we propose a new methodology for constructing numerical integrators with high weak order for the time integration of stochastic differential equations. This approach is illustrated with the constructions of new methods of weak order two, in particular, semi-implicit integrators well suited for stiff (meansquare stable...