Alternating Direction Implicit Orthogonal Spline Collocation Methods for Solving Initial/Boundary Value Problems

Abstract

The primary focus of this project was on the analysis and development of new parallel algorithms for the solution of linear and nonlinear initial/boundary value problems (IBVPs) in two space variables. Parabolic, second order hyperbolic, biharmonic, and Schrodinger type problems were considered. The new algorithms, which are alternating direction implicit (ADI) orthogonal spline collocation (OSC) methods employing C1 piecewise polynomial spaces of arbitrary order, have been implemented and their efficacy was demonstrated on test problems taken from the literature. Rigorous stability and convergence analyses of the methods were also carried out.

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Document Details

Document Type
Technical Report
Publication Date
Nov 11, 1998
Accession Number
ADA357879

Entities

People

  • Bernard Bialecki
  • Graeme Fairweather

Organizations

  • University of Kentucky

Tags

Communities of Interest

  • Human Systems

DTIC Thesaurus Topics

  • Accuracy
  • Algorithms
  • Boundaries
  • Boundary Value Problems
  • Coefficients
  • Convergence
  • Differential Equations
  • Equations
  • Errors
  • Galerkin Method
  • Kentucky
  • Linear Systems
  • Partial Differential Equations
  • Polynomials
  • Quantum Mechanics
  • Scientists
  • Students

Fields of Study

  • Mathematics

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)

Technology Areas

  • Space