I will go shopping on Sunday.(Sunday指的是这个星期天)/ I went shoppingon Sunday (Sunday 指的是上一个星期天)

两句都没加the,说明星期有就近指代功能,它伴随动作时间的变化而变化。

那样He died on the Sunday of the car accident.这句为何不能随时间变化而变化,必须要加the呢?   假如如此的话,I went shopping on Sunday atthe end of last month 这句加the吗?

I went shopping on Sunday at the end of last month. 这里Sunday 前不需要the, 由于at the end of last month 一般看作状语。在乎思上=on the last Sunday of last month.