Differential Equations

Boundary condition	Elliptic	Hyperbolic	Parabolic
	Laplace, Poisson in (x, y)	Wave equation in (x, t)	Diffusion equation in (x, t)
Cauchy
Open surface	Unphysical results (instability)	Unique, stable solution	Too restrictive
Closed surface	Too restrictive	Too restrictive	Too restrictive
Dirichlet
Open surface	Insufficient	Insufficient	Unique, stable solution
Closed surface	Unique, stable solution	Solution not unique	Too restrictive
Neumann
Open surface	Insufficient	Insufficient	Unique, stable solution
Closed surface	Unique, stable solution	Solution not unique	Too restrictive

TBA

Ordinary Differential Equations

First-Order Equations

Second-Order Equations

Series Solutions

Partial Differential Equations

First-Order Equations

Second-Order Equations

Separation of Variables

Laplace and Poisson Equations

Wave Equation

Dispersive PDEs

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Related Topics

• [Scientific Computation with Python, Matlab and Mathematica]
• Numerical Methods to solve PDEs

References

Differential Equation

ODE

PDE

Dispersive PDEs

Mathematical Methods for Physicists, Arfken

Some lecture notes