Ryan I. Fernandes

An alternating direction Galerkin method for a class of second-order hyperbolic equations in two space variables

A new alternating-direction implicit (ADI) Galerkin method is devised and analyzed for solving a certain class of second-order hyperbolic initial-boundary value problems in two space variables. This class includes the wave equation in Cartesian coordinates, polar coordinates, and cylindrical coordinates with radial symmetry. Optimal a priori

Alternating Direction Implicit Orthogonal Spline Collocation Methods for an Evolution Equation with a Positive-Type Memory Term

H_0^1

An Orthogonal Spline Collocation Alternating Direction Implicit Crank--Nicolson Method for Linear Parabolic Problems on Rectangles

and

An Alternating-Direction Implicit Orthogonal Spline Collocation Scheme for Nonlinear Parabolic Problems on Rectangular Polygons

L^2

Orthogonal spline collocation Laplace-modified and alternating-direction methods for parabolic problems on rectangles

-error estimates are derived.

An ADI extrapolated Crank-Nicolson orthogonal spline collocation method for nonlinear reaction-diffusion systems

New numerical techniques are presented for the solution of a class of linear partial integro-differential equations (PIDEs) with a positive-type memory term in the unit square. In these methods, orthogonal spline collocation (OSC) is used for the spatial discretization, and, for the time stepping, new alternating direction implicit (ADI) methods based on the backward Euler, the Crank-Nicolson, and the second order BDF methods combined with judiciously chosen quadrature rules are considered. The ADI OSC methods are proved to be of optimal accuracy in time and in the

On the parallelization of a comprehensive regional-scale air quality model

L^2

An Alternating Direction Implicit Backward Differentiation Orthogonal Spline Collocation Method for Linear Variable Coefficient Parabolic Equations

norm in space. Numerical results confirm the predicted convergence rates and also exhibit optimal accuracy in the

An ADI extrapolated Crank-Nicolson orthogonal spline collocation method for nonlinear reaction-diffusion systems on evolving domains

L^{\infty}

Alternating direction implicit orthogonal spline collocation on some non-rectangular regions with inconsistent partitions

and