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What is the global solution of an ordinary differential equation?
The global solution of an ordinary differential equation (ODE) is a solution of which there are no extensions; i.e. you can't add a solution to the global solution to make it more general, the global solution is as general as it gets.
What is the general solution of a differential equation?
It is the solution of a differential equation without there being any restrictions on the variables (No boundary conditions are given). Presence of arbitrary constants indicates a general solution, the number of arbitrary constants depending on the order of the differential equation.
What is a numerical solution of a partial differential equation?
Some partial differential equations do not have analytical solutions. These can only be solved numerically.
Why you need the numerical solution of partial differential equations?
Very often because no analytical solution is available.
What is the local solution of an ordinary differential equation?
The local solution of an ordinary differential equation (ODE) is the solution you get at a specific point of the function involved in the differential equation. One can Taylor expand the function at this point, turning non-linear ODEs into linear ones, if needed, to find the behavior of the solution around that one specific point. Of course, a local solution tells you very little about the ODE's global solution, but sometimes you don't want to know that anyways.
