Collocation Method to Solve Elliptic Equations, Bivariate Poly-Sinc Approximation

Abstract

The paper proposes a collocation method to solve bivariate elliptic
partial differential equations. The method uses Lagrange approximation
based on Sinc point collocations. The proposed approximation is collocat-
ing on non-equidistant interpolation points generated by conformal maps,
called Sinc points. We prove the upper bound of the error for the bivariate
Lagrange approximation at these Sinc points. Then we define a colloca-
tion algorithm using this approximation to solve elliptic PDEs. We verify
the Poly-Sinc technique for different elliptic equations and compare the
approximate solutions with exact solutions.