An euler-type method for two-dimensional volterra integral equations of the first kind

Sean McKee*, Tao TANG, Teresa Diogo

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

41 Citations (Scopus)

Abstract

Two-dimensional first-kind Volterra integral equations (VIEs) are studied. The first-kind equations are reduced to second kind, and by obtaining an appropriate integral inequality, existence and uniqueness are demonstrated. The equivalent discrete integral inequality then permits convergence of discretization methods; and this is illustrated for the Euler method. Finally, a class of nonlinear telegraph equations is shown to be equivalent to (two-dimensional) Volterra integral equations, thereby providing existence and uniqueness results for this class of equations. Furthermore, the telegraph equation may be solved by the numerical method for two-dimensional VIEs, and a simple numerical example is given.

Original languageEnglish
Pages (from-to)423-440
Number of pages18
JournalIMA Journal of Numerical Analysis
Volume20
Issue number3
DOIs
Publication statusPublished - Jul 2000

Scopus Subject Areas

  • Mathematics(all)
  • Computational Mathematics
  • Applied Mathematics

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