On the instability of leap-frog and Crank-Nicolson approximations of a nonlinear partial differential equation Journal Article uri icon



  • It is well known that nonlinear instabilities may occur when the partial differential equations, describing, for example, hydrodynamic flows, are approximated by finite-difference schemes, even if the corresponding linearized equations are stable. A scalar model equation is studied, and it is proved that methods of leap-frog and Crank-Nicolson type are unstable, unless the differential equation is rewritten to make the approximations quasi-conservative. The local structure of the instabilities is discussed.

publication date

  • January 1, 1973

has restriction

  • bronze

Date in CU Experts

  • November 4, 2020 8:03 AM

Full Author List

  • Fornberg B

author count

  • 1

Other Profiles

International Standard Serial Number (ISSN)

  • 0025-5718

Electronic International Standard Serial Number (EISSN)

  • 1088-6842

Additional Document Info

start page

  • 45

end page

  • 57


  • 27


  • 121