Abstract
Initial-boundary value problems for hyperbolic and parabolic partial differential equations with Diriclilet boundary conditions are considered by the method of lines approach in an arbitrarily given domain D in 2-D or 3-D. With D embedded in a rectangular domain, a new high order method for the space discretization problem is constructed in D by employing a Fourier collocation method in a uniform Cartesian system of gridpoints. Singularities are systematically removed by utilizing properties of the Bernoulli polynomials. Theoretical estimates for the accuracy of the method are established. The estimates are confirmed by numerical experiments for simple approximation problems.
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