methods of solving ODE

There are many different methods of solving ordinary differential equations that occur in physics. These are tabulated here and divided into sections for linear and non-linear ODEs. These sections are further subdivided into exact, numerical and quantitative methods.

1 Linear ODEs

1.1 Exact methods

• General solution of linear differential equation
• Linear differential equation of first order
• Method of separation of variables
• Method of integrating factors
• Method of undetermined coefficients
• Frobenius’ method
• Method of Green’s functions

1.2 Numerical methods

• Runge-Kutta method
• Heun method
• Rayleigh-Ritz method
• Monte Carlo methods

1.3 Quantitative methods

2 Non-linear ODEs