The Generalized Fourier Series Method

The book presents and explains a general, efficient, and elegant method of approximate solution for boundary value problems for an elliptic system of partial differential equations arising in elasticity theory. The methodology for constructing generalized Fourier series based on the structure of the problem is shown in detail, and all the attending mathematical properties are derived with full rigor. A numerical scheme directly related to the series method is developed and employed to compute approximate solutions, illustrated by a variety of examples.

Inhalt

1. The Mathematical Model.- 2. Generalized Fourier Series.- 3. Interior Dirichlet Problem.- 4. Interior Neumann Problem.- 5. Interior Robin Problem.- 6. Exterior Dirichlet Problem.- 7. Exterior Neumann Problem.- 8. Exterior Robin Problem.- A. Numerical Issues.- B. Numerical Integration.- C. Interior Boundary Value Problem for D[x,y].- D. Exterior Boundary Value Problems for D^A[X,y].- E. Numerical Integration of P[x,y] and P^A[x,y].- References.- Index.