Separate HTML for Scripted Foil 7 What Conditions are sufficient for solution of PDE's -- Cauchy Boundary Conditions and Hyperbolic,Parabolic and Elliptic PDE's

Basic HTML version of Foils prepared 8 November 1995

Foil 7 What Conditions are sufficient for solution of PDE's -- Cauchy Boundary Conditions and Hyperbolic,Parabolic and Elliptic PDE's

From CPS615 Module on Iterative PDE Solvers CPS615 Basic Simulation Track for Computational Science -- Fall Semester 95. by Geoffrey C. Fox

Cauchy conditions

y and śy/śn are given

on a curve

Solution given by Taylor series for each point near curve if these are sufficient to determine higher derivatives

Consider general form of PDE:

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