Numerical Solutions Of Partial Differential Equations.pdf

文档介绍：NUMERICAL SOLUTION OF P AR TIAL
DIFFERENTIAL EQUA TIONS
MA
LECTURE NOTES
B
Neta Departmen t of Mathematics
Na v al P ostgraduate Sc ho ol
Co de MA
Nd
Mon terey
California
Marc h
c

Professor Ben a

Con ten ts
In tro duction and Applications

Basic Concepts and De
nitions

Applications

Conduction of Heat inaRod


Boundary Conditions

A Vibrating String

Boundary Conditions


Di
usion in Three Dimensions

Separation of V ariables
Homogeneous Equations

P arab olic equation in one dimension

Other Homogeneous Boundary Conditions

Eigen v alues and Eigenfunctions

F ourier Series

In tro duction


Orthogonalit y

Computation of Co e
cien ts

Relationship to Least Squares

Con v ergence


F ourier Cosine and Sine Series

F ull solution of Sev eral Problems

PDEs in Higher Dimensions

In tro duction


Heat Flo w in a Rectangular Domain

Vibrations of a rectangular Mem brane

Helmholtz Equation

Vibrating Circular Mem brane

Laplace
s Equation in a Circular Cylinder

Laplace
s equation in a sphere

Separation of V ariables
Nonhomogeneous Problems