Mathematics 625 Spring, 1997

PDE Classifications

Partial differential equations can be classified according to the type of subsidiary conditions that must be imposed to produce a well posed problem. Consider a general linear second order PDE in two independent variables of the form

Au_xx + 2Bu_xy + Cu_yy + Du_x + Eu_y + Fu + G = 0,

A	B
B	C

Textbook

K. Eriksson, D. Estep, P. Hansbo, and C. Johnson, Computational Differential Equations, Cambridge University Press, Cambridge, UK, 1996.

Companion Software

Femlib is an interactive program for the numerical solution of ordinary and partial differential equations based on the Finite Element Method in adaptive form with automatic error control.

Other Books of Interest

C. DeBoor, A Proctical Guide to Splines, Springer-Verlag, New York, NY, 1978.

G. E. Forsythe and W. R. Wasow, Finite-Difference Methods for Partial Differential Equations, John Wiley & Sons, New York, NY, 1960.

C. Johnson, Numerical Solution of Partial Differential Equations by the Finite Element Method, Cambridge University Press, Cambridge, UK, 1990.

L.o Lapidusand G. F. Pinder, Numerical Solution of Partial Differential Equations in Science and Engineering, John Wiley & Sons, New York, NY, 1982.

M. H. Schultz, Spline Analysis, Prentice-Hall, Englewood Cliffs, NJ, 1973.

G. Strang and G. J. Fix, An Analysis of the Finite Element Method, Prentice-Hall, Englewood Cliffs, NJ, 1973.

Y. W. Kwon and H. Bang, The Finite Element Method Using MATLAB, CRC Press, Boca Raton, FL, 1997.

R. S. Varga, Matrix Iterative Analysis, Prentice-Hall, Englewood Cliffs, NJ, 1962.

B. Wendroff, First Principles of Numerical Analysis, Addison-Wesley, Reading, MA, 1969.

Homework

	Assignment	Due date
	a1	February 18
	a2	February 27
	a3	April 1
	a4	April 24
	a5	May 1

Cheers,
Craig C. Douglas