ABSTRACT
This chapter introduces some of the main ideas of special spectral method. It begins by examining the Dirichlet problem for a symmetric elliptic partial differential equation. The chapter presents a spectral method for this problem and for similar linear and nonlinear problems with a variety of boundary conditions. It compares the illustrative example with the use of the finite element method as implemented in Matlab. The program uses a piecewise linear approximation over triangular elements. To obtain an error comparable to our spectral method required 186,368 triangles, and the number of nodes was 93,697.
