Simple method to lengthen alkane?
The procedure to convert methane to longer hydrocarbons at low temperature is one of the so-called Holy Grails in catalysis (http://pubs.acs.org/doi/abs/10.1021/ar00051a001). The person who is able to invent a process wherein this is possible (at an efficient rate) would be a very good candidate for a Nobel Prize. 

Why is it then so difficult to convert methane to longer hydrocarbons? Methane is a highly stable molecule. In order to form a longer hydrocarbon, methane first has to be broken down to smaller CH$_{x}$ fragments. The first dehydrogenation step of methane (to CH$_{3}$) has a very high activation energy and even using a good catalyst, this is not feasible at an appreciable rate under 100 degrees celcius.

Industrially, this process is done by first creating synthesis gas (CO + H$_{2}$) from methane by partial oxidation using pure oxygen (which is cryogenically separated from air). Thereafter, the synthesis gas is compressed to roughly 20 atm of pressure and converted to very long hydrocarbons (waxes) in the Fischer-Tropsch process. In turn, these waxes are cracked to form diesel fuels and lubricants. 

I am afraid that there is no easy way of converting methane to longer hydrocarbons. Though please keep trying because basically the whole world would benefit if you succeed! :-)