Separate Focus 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

1	Cauchy conditions
2	y and śy/śn 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