Simulations require supercomputers for doing large scale, detailed calculations, but simple situations can be solved completely analytically. For example, gravitational time dilation can be calculated somewhat simply for a central gravitational potential: https://en.wikipedia.org/wiki/Gravitational_time_dilation#Ou...
General Relativity is incredibly math heavy but fundamentally the numerical methods involved are standard methods for differential equations. The hard part is going from the math to a solvable form. See https://arxiv.org/pdf/2008.12931 for a broad overview. This will of course probably not make sense without an introduction to differential geometry, a beast of a topic itself. See some big textbook like https://arxiv.org/pdf/2412.08026 or find yourself a copy of Gravitation by Misner, Thorne and Wheeler.
...which uses Scheme to teach differential geometry. I would need to learn quite a bit more before tackling that book. Maybe something like: "Structure and Interpretation of Classical Mechanics"?
General Relativity is incredibly math heavy but fundamentally the numerical methods involved are standard methods for differential equations. The hard part is going from the math to a solvable form. See https://arxiv.org/pdf/2008.12931 for a broad overview. This will of course probably not make sense without an introduction to differential geometry, a beast of a topic itself. See some big textbook like https://arxiv.org/pdf/2412.08026 or find yourself a copy of Gravitation by Misner, Thorne and Wheeler.