Solving partial differential equations with point collocation and one-dimensional integrated interpolation schemes

Abstract

[Summary]: This lecture presents an overview of the Integral Collocation formulation for numerically solving partial differential equations (PDEs). However, due to space limitation, the paper only describes the latest development, namely schemes based only on one-dimensional (1D) integrated interpolation even in multi-dimensional problems. The proposed technique is examined with Chebyshev polynomials and radial basis functions (RBFs). The latter can be used in both regular and irregular domains. For both basis functions, the accuracy and convergence rates of the new technique are better than those of the differential formulation.