Different buffer size for different serial port of Mega2560 ?

Thanks Koepel !

I have little knowledges about Rx & Tx communication. If the Arduino Tx never misses data, what is the purpose of Tx buffer ?

My display is something like https://www.ebay.com/itm/2-2-inch-USART-HMI-Intelligent-Serial-Port-Integrated-GPU-TFT-LCD-Module-240-320-/262739647872 ,
which has embeded processor. It communicate with Arduino with Rx & Tx with syntax like :

DS16(x,y,'Any long strings ....',c); where (x,y) are pixel position.

I know the problem is in the display module, it is not fast enough to receive data. For example, if I write one row of messages, there is no problem. But if need to refresh several rows of data, some data will be missed in the display. On the other hand, if I insert some delay between the data sends, the display is fine.

You may think that I can just use the delay to fixed this problem. But my project is a arpeggiator with real time control and real time display, if the delay is too much, the playback will be sluggish !

Concerning the memory usage, memory is always insufficient for me ! If there is more memory, I can add more features to my project !