The direct matrix solver is the fastest solver. However, it requires a lot of memory. The memory requirement increases with the the number of grid points. However, this is not a linear increase. It increases approximately as x^2*y where x is the number of points along the x-axis and y is the number of points along the y-axis. For example, with x=100 and y=500 would require 128MB. Therefore, it is easy to exceed the memory limits of the computer. To conserve memory, you should carefully design the grid such that there are as few x points as possible.
The iterative solver requires much less memory, but it is much slower. The memory requirement increases only linearly with the number of grid points. However, the time required to complete a calculation increases as the square of the grid points.
It is better to start with the direct solver first unless the memory requirement is greater than 3GB. Any jobs requiring more than 3GB will not be executed by the computer.