| Method | Typical Fortran 77 Implementation | |-----------------------|------------------------------------------------------------| | Gaussian elimination | Two nested DO loops, partial pivoting, implicit none optional | | LU decomposition | Subroutine with work arrays passed via common or arguments | | Newton–Raphson | External function, derivative approximation or analytic | | Runge–Kutta (4th order)| Subroutine with step control, common block for parameters | | Tridiagonal solver (Thomas) | Efficient, using fixed-size arrays and direct indexing |
Example snippet from a hypothetical section (Gaussian elimination):