Stability Analysis of Difference Schemes for Variable Coefficient Schrodinger Type Equations.

Abstract

This document considers the stability of difference schemes for the solution of the initial boundary value problem for equation where u, A, B, c and f are complex valued functions. Using energy methods, the author establish the stability of a general two level scheme which includes Euler's method, Crank-Nicolson's method and the backward Euler method. If the coefficient A(x,t) is purely imaginary, the explicit Euler's method is unconditionally unstable. For this case, their propose a new scheme with appropriately chosen artificial dissipation, which is proven to be conditionally stable.

Open PDF

Document Details

Document Type
Technical Report
Publication Date
Sep 01, 1985
Accession Number
ADA161989

Entities

People

  • Longjun Shen
  • Tony F. Chan

Organizations

  • Yale University

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Acoustics
  • Boundaries
  • Boundary Value Problems
  • Cauchy Problem
  • Coefficients
  • Contracts
  • Difference Equations
  • Differential Equations
  • Equations
  • Fourier Analysis
  • Intervals
  • Military Research
  • Parallel Computing
  • Polynomials
  • Two Dimensional
  • Underwater Acoustics

Fields of Study

  • Mathematics

Readers

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