The Application of Sparse Matrix Methods to the Numerical Solution of Nonlinear Elliptic Partial Differential Equations.

Abstract

The authors present a new algorithm for solving general semilinear, elliptic partial differential equations. The algorithm is based on Newton's Method but uses an approximate iterative method to solve the linear systems that arise at each step of Newton's Method. The authors show that the algorithm can maintain the quadratic convergence of Newton's Method and that it may be substantially faster than other available methods for semilinear or nonlinear partial differential equations.

Document Details

Document Type
Technical Report
Publication Date
Feb 01, 1974
Accession Number
ADA017591

Entities

People

  • A. H. Sherman
  • Martin H. Schultz
  • S. C. Eisenstat

Organizations

  • Yale University

Tags

DTIC Thesaurus Topics

  • Algorithms
  • Convergence
  • Differential Equations
  • Equations
  • Linear Systems
  • Mathematics
  • Partial Differential Equations
  • Sparse Matrix

Fields of Study

  • Mathematics

Readers

  • Adaptive Control and Estimation with Uncertainty in Dynamic Systems.