# Discretizing time term for PDEs

I am actually confused about time stepping for PDEs. Before, I was distretizing time using backward Euler method for implicit formulation and I get a system of Algebraic equations to solve. Now during my research when I read papers, I find they disctretize space only leaving time derivative which yields system ODEs? What is the difference between two approaches and when I use one not another?

• Jun 29 '16 at 7:40

The technique of discretising the spatial derivatives in a problem and leaving the temporal evolution as continuous is known as the "method of lines", there's lots of stuff on google about it, e.g. http://www.scholarpedia.org/article/Method_of_lines. It's known as the method of lines because you literally solve the problem by solving individual equations (ODEs) along lines of constant $x$ (say).