You can use convolution to “sample” the frequency response of your Yamaha speakers. But that won’t work for capturing the “non-linear behavior” of the speaker (non-linear = the way it saturates / distorts when driven with high gains). There is no easy way to capture and recreate this effect, but you can of course simply make use of the many great saturators and other effects that are already available out there.
So just use a convolution engine + impulse responses of small speakers loaded into it at 100% wet (you could also try guitar cabs) + saturation plugin (Klanghelm IVGI, Voxengo TubeAmp and Klevgrand FreeAmp are all free and very good). This will get you there.
If you want to create such an effect completely all by yourself without using existing plugins, I propose you catch up on your college level maths, learn all about C++ and start to study DSP audio development full time. It will take you at least 5 years of full time study until you get to a point where you are capable of coding emulations of real analog gear.