A fully Galerkin method in both space and time is developed for the second-order, linear hyperbolic problem. Sinc basis functions are used and error bounds are given which show the exponential convergence rate of the method. The matrices necessary for the formulation of the discrete system are easily assembled. They require no numerical integrations (merely point evaluations) to be filled. The discrete problem is formulated in two different ways and solution techniques for each are described. Consideration of the two formulations is motivated by the computational architecture available. Each has advantages for the appropriate hardware. Numerical results reported show that if 2N + 1 basis functions are used then the exponential convergence rate q e x p ( -~f i ) J , K > 0, is attained for both analytic and singular problems.

Summary. The Sinc-Galerkin method is applied to the canonical forms of second order partial differential equations in multiple space dimensions. For time dependent problems the scheme is fully Galerkin; i.e., the domain of the basis elements includes time. Hence the approximate solution for each equation is specified by solving the associated linear system. Notation is developed which facilitates description of both the linear systems and the algorithms used to solve them. Alternative algorithms are offered dependent on a scalar versus vector computing environment. Numerical results for the test problems presented sustain the exponential convergence rate of the method even in the presence of singularities.

No abstract

No abstract

No abstract

No abstract

No abstract

Several methods are presented for solving separable elliptic partial differential equations over an irregular region B using alternating direction collocation on a rectangular grid over an embedding rectangle R. The methods are geometric predictor-corrector schemes. At each iterative step, the numerical solution is predicted on R via a full AD1 sweep. The forcing term is then updated (corrected) on collocation points interior to B. By this means, the geometry of B and boundary conditions on aB are approximated implicitly using rectangular grids on R.