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PY3CO2 Part I Partial Differential Equations



I Introduction
Introduction to PDE's, Boundary Conditions and Initial Conditions
Coordinate Systems and Differential Operators

Survey of PDE's in Physical Applications

II Elliptic PDE's
Poisson and Laplace Equations, Solution by Integral Transform, Finite Difference Method for Differential Operators, Liebmann's Method applied to Poisson's equation

III Parabolic PDE's
Computer Modelling of Fluids, Advection and Diffusion, Continuity Equation, Diffusion Equation, Schrodinger Equation as a Diffusion Equation , Method of Separation of Variables, Solving Inhomogeneous PDE's by Eigenfunction Expansion

IV Hyperbolic PDE's
1-D Wave Equation, Finite Difference Methods for Parabolic and Hyperbolic PDE's, Explicit Method, Implicit Crank-Nicholson Method, Waves in Channels, Solution of Coupled Nonlinear Wave Equations by Finite Differences, Solitary Waves and the Korteweg-deVries Equation

V Classification of PDE's

VI Stability of Numerical Methods for PDE's
Fourier Stability Method, Matrix Stability Method

Course texts:

Partial Differential Equations for Scientists and Engineers
S.J. Farlow, Dover (1993) S-LEN 515.353 M23; 3

Partial Differential Equations for Scientists and Engineers
G. Stephenson, Imperial College Press, (1996) 515.353 N8

Computational Physics, Problem Solving with Computers
R.H. Landau and M.J. Paez, Wiley (1997) 530.07 N7

notes I

Links to soliton websites

C source files



Implicit Algorithm

Linearised wave equation

Nonlinear wave equation

Korteweg-deVries equation

Korteweg-deVries equation Implicit algorithm



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Last updated: Apr 30 2012.

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