HTML version of Scripted Foils prepared 11 November 1996

Foil 8 What Conditions are sufficient for solution of PDE's -- Cauchy Boundary Conditions and Hyperbolic,Parabolic and Elliptic PDE's

From CPS615-Basic PDE Solver Discussion and Sparse Matrix Formulation Delivered Lectures of CPS615 Basic Simulation Track for Computational Science -- 8 November 96. by Geoffrey C. Fox *
Secs 288
1 Cauchy conditions
2 y and ¶y/¶n are given
3 on a curve
4 Solution given by Taylor series for each point near curve if these are sufficient to determine higher derivatives
  • Consider general form of PDE:
5 Can be solved as linear system with deterministic equations for derivatives of boundary conditions if coefficients have certain characteristics -- Gives rise to three types:
  • b2>4ac hyperbolic equations -- Above strategy works
  • b2=4ac parabolic equations
  • b2<4ac elliptic equations
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