How to represent calls within same class using UML-Sequence diagram

Representing a self-call on a UML sequence diagram (see step 7).

If the called method is (or should be) private, then it can safely be excluded from the sequence diagram as an implementation detail.

However I smell the God-Class anti pattern; your class has multiple responsibilities and should be deconstructed. Break down the class so that is has only a single responsibility using delegation. Those method calls would be a good starting point.

It is actually possible to refer to the self instance

In fact UML spec 2.5b1 page 607, about a Lifeline is said: If the name is the keyword self, then the Lifeline represents the object of the classifier that encloses the Interaction that owns the Lifeline. Ports of the encloser may be shown separately even when self is included.

See https://web.archive.org/web/20131101211441/http://lowcoupling.com/post/47844944042/uml-sequence-diagrams for a complete example

A few suggestions:

1. You can show successive methods on a sequence diagram using self calls. See Figure 1 here for an example (self calls are the circular invocations on the same lifeline).
2. As an alternative you might consider an Activity Diagram. Possibly better suited for illustrating order of methods.
3. Refactor the code. Lots of logic in a single class is usually a bad smell. Assuming you have the scope, refactoring might be a good idea.

hth.