In software engineering, what's the name of a development process like the waterfall model, but with more cycles? Does something like this exist?
In my case, I developed the parts of my application separately and went through all the steps in the waterfall model (requirements, analysis, design, implementation, testing). At the end I put everything together.
Is it wrong to call it waterfall process with 4 cycles?
It sounds like you are describing what Steve McConnell called Waterfall with Subprojects. In this methodology, you waterfall through conceptualization, requirements engineering, and architectural design. Then, for every major component, you then proceed through a detailed design, coding, and testing phase. At the end, you integrate the components in a system testing phase.
Typically, this is done by multiple teams at the same time, each working on a separate component. However, because you were working alone, it probably resembled a more iterative approach. The key difference between Waterfall with Subprojects and a true iterative approach is when you do the integration. In Waterfall with Subprojects, it comes at the completion of all subprojects. With a truly iterative approach, it happens continuously and you are fully integrated at the end of every iteration.
I believe what you're looking for is The Spiral Model. From the wikipedia page, "The spiral model combines the idea of iterative development (prototyping) with the systematic, controlled aspects of the waterfall model. "
In my opinion you described a typical iterative and incremental development process but this actually depends on the definition of "parts of my application." If you consider every part of the application as a atomic entity with its own life-cycle (integration, maintenance, decommissioning, etc), then yes, you have 4 separate projects each of which is developed using waterfall process.
Updated following your commend:
From wait you are saying it seems like you are talking about development of 4 subsystems but the final output is a system, which depends on the other 4. If you subsystems don't have their own life cycle (including integration, etc) then you cannot define the whole process as 4 parallel waterfall processes.
