| D01AHF | One-dimensional quadrature, adaptive, finite interval, strategy due to Patterson, suitable for well-behaved integrands |
| D01AJF | One-dimensional quadrature, adaptive, finite interval, strategy due to Piessens and de Doncker, allowing for badly behaved integrands |
| D01AKF | One-dimensional quadrature, adaptive, finite interval, method suitable for oscillating functions |
| D01ALF | One-dimensional quadrature, adaptive, finite interval, allowing for singularities at user-specified break-points |
| D01ANF | One-dimensional quadrature, adaptive, finite interval, weight function cos(ωx) or sin(ωx) |
| D01APF | One-dimensional quadrature, adaptive, finite interval, weight function with end-point singularities of algebraico-logarithmic type |
| D01AQF | One-dimensional quadrature, adaptive, finite interval, weight function 1/(x-c), Cauchy principal value (Hilbert transform) |
| D01ARF | One-dimensional quadrature, non-adaptive, finite interval with provision for indefinite integrals |
| D01ATF | One-dimensional quadrature, adaptive, finite interval, variant of D01AJF efficient on vector machines |
| D01AUF | One-dimensional quadrature, adaptive, finite interval, variant of D01AKF efficient on vector machines |
| D01BDF | One-dimensional quadrature, non-adaptive, finite interval |
| D01DAF | Two-dimensional quadrature, finite region |
| D02GAF | ODEs, boundary value problem, finite difference technique with deferred correction, simple nonlinear problem |
| D02GBF | ODEs, boundary value problem, finite difference technique with deferred correction, general linear problem |
| D02KAF | Second-order Sturm–Liouville problem, regular system, finite range, eigenvalue only |
| D02KDF | Second-order Sturm–Liouville problem, regular/singular system, finite/infinite range, eigenvalue only, user-specified break-points |
| D02KEF | Second-order Sturm–Liouville problem, regular/singular system, finite/infinite range, eigenvalue and eigenfunction, user-specified break-points |
| D02RAF | ODEs, general nonlinear boundary value problem, finite difference technique with deferred correction, continuation facility |
| D03EBF | Elliptic PDE, solution of finite difference equations by SIP, five-point two-dimensional molecule, iterate to convergence |
| D03ECF | Elliptic PDE, solution of finite difference equations by SIP for seven-point three-dimensional molecule, iterate to convergence |
| D03EDF | Elliptic PDE, solution of finite difference equations by a multigrid technique |
| D03NCF | Finite difference solution of the Black–Scholes equations |
| D03PCF | General system of parabolic PDEs, method of lines, finite differences, one space variable |
| D03PHF | General system of parabolic PDEs, coupled DAEs, method of lines, finite differences, one space variable |
| D03PPF | General system of parabolic PDEs, coupled DAEs, method of lines, finite differences, remeshing, one space variable |
| D03RAF | General system of second-order PDEs, method of lines, finite differences, remeshing, two space variables, rectangular region |
| D03RBF | General system of second-order PDEs, method of lines, finite differences, remeshing, two space variables, rectilinear region |
| D03UAF | Elliptic PDE, solution of finite difference equations by SIP, five-point two-dimensional molecule, one iteration |
| D03UBF | Elliptic PDE, solution of finite difference equations by SIP, seven-point three-dimensional molecule, one iteration |