Explicit Program Solutions of PDE via Sinc–Pack
Separation of Variables is the unifying theme of this chapter, wherein multidimensional problems over curvilinear regions can be reduced to solving a relatively small number of corresponding one dimensional problems. In §4.2 solutions are analytic continuations, hence harmonic continuations, of Sinc functions. In other sections we obtain particular solutions of non-homogeneous PDE through Sinc evaluation of linear and nonlinear convolution integrals over rectangular and curvilinear regions. The solution to the PDE including boundary conditions is then obtained using the boundary integral equation (BIE) method. Convergence will seen to be exponential and absolute error is uniform throughout the entire region.