How does partial melting explain mafic magmas at divergent boundaries and intermediate/felsic magmas at subduction zones?
It would help to understand the process of whats going on here. At convergent boundaries, think of these areas as crustal recycling centers. This is where the old crust is being subducted back down into the mantle, where the crustal rocks are melted down into magma once again. This is where your higher temperatures are generated, in excess of 1300 degrees Celsius. This type of magma, called mafic magma, produces basalt, generally has a silicon dioxide content of less than 50%, and produces quiet eruptions, due to the low silica content. Divergent boundaries use this type of magma to create new sea floor in the middle of the rift mountains.
The other type of magma, felsic magma, is an intermediate type of magma, the product of partial melts in continental rift zones and hotspots, such as Yellowstone National Park. This type of magma has a significantly higher silicon dioxide content, better than 70%, causing it to produce violent, explosive eruptions. The magma typically is lower in temperature than mafic magma, usually under 900 degrees Celsius, and has a higher degree of plasticity than does mafic magma, giving it the term "intermediate magma".