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Parallel numerical algorithms are presented for the solution of fourth-order parabolic equations. The algorithms are tested on three problems with timedependent and time-independent boundary conditions. KEY WORDS: Fourth-order parabolic equations, complex splittings, parallel algorithms, Pad6 approximants.C.R. CATEGORIES: G.1.8.

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SUMMARY Techniques for two-time level difference schemes are presented for the numerical solution of first-order hyperbolic partial differential equations. The space derivative is approximated by (i) a low-order, and (ii) a higher-order backward difference replacement, resulting in a system of first-order ordinary differential equations, the solutions of which satisfy recurrence relations. The methods are obtained from the recurrence relations and are tested on three linear problems and one non-linear problem from the literature.KEY WORDS hyperbolic equations; finite-difference methods; Pad6 approximants; sequential and parallel implementation