Recurrence solution of a block tridlagonal matrix equation with neumann, dirichlet, mixed or periodic boundary conditions

Abstract

Title of program: PERDIAG Nature of physicalproblem A theorist may wish to solve the matrix equation A U = W, Catalogue number: AARF rapidly, where A is a block tridiagonal matrix. This type of matrix equation frequently arises in the solution ofproblems Program obtainable from: CPC Program Library, Queen’s in one space dimension; in the solution of boundary-value University of Belfast, N. Ireland (see application form in this and many initial-value problems (because the time-dependent issue) problem has been formulated implicitly), where it is necessary to solve n coupled, finite diff~renceequations. The program Computer: CDC 6500; Installation: Imperial College Cornis capable of dealing with Nei~rnann,Dirichlet, mixed or puter Centre periodic boundary conditions. If the boundary conditions are periodic, the resulting matrix A is block tridiagonal with addiOperating system: NOS tional blocks in the upper right and left corners, referred to here asblock perdiagonal. Programming language used: FORTRAN IV Method of solution High speed storage required: 17.7 Kwords A recurrence solution is used to solve the matrix equation A U = W. The method follows the principles for a recurrence No. of bits in a word: 60 solution of a tridiagonal matrix equation [1], modified, when appropriate, to deal with the more complex case of periodic Overlay structure: none boundary conditions.