ABSTRACT
This chapter provides solutions to nonlinear equations using multivariate polynomials on the unit ball. It discusses spectral method for the nonlinear Dirichlet problem with numerical examples. The chapter also provides reference solution for Fisher’s equation. In convergence analysis, Osborn converted a finite element method for solving an eigenvalue problem for an elliptic partial differential equation to a corresponding numerical method for approximating the eigenvalues of a compact integral operator. He then used results for the latter to obtain convergence results for his finite element method.
