You can't access non-static variables in static methods. Refer to the documentation:
While an instance of a class contains a separate copy of all instance fields of the class, there is only one copy of each static field.
It is not possible to use this to reference static methods or property accessors.
In this case, if your update method (BTW should be Update) needs to access non-static members of your class, you should make it non-static, and change the Form2 as follows:
1) Add a field and change form's constructor to accept Form1 instance as a parameter:
private Form1 form1;
public Form2(Form1 form1)
{
this.form1 = form1;
}
2) When creating form2 from form1 pass its instance:
Form2 form2 = new Form2(this); // when in Form1
If you're creating Form2 in some other context you need to (analogically) have form1 instance at hand and call:
Form2 form2 = new Form2(form1);
3) Change the event handler to work on the particular instance of Form1:
public button1_click()
{
this.form1.update();
}