## D02 – Ordinary Differential Equations

• D02 Introduction
• D02 Introduction to the 'mn' routines
• d02ag – Ordinary differential equations, boundary value problem, shooting and matching technique, allowing interior matching point, general parameters to be determined
• nag_ode_bvp_shoot_genpar_intern – d02ag
• d02bg – Ordinary differential equations, initial value problem, Runge–Kutta–Merson method, until a component attains given value (simple driver)
• nag_ode_ivp_rkm_val_simple – d02bg
• d02bh – Ordinary differential equations, initial value problem, Runge–Kutta–Merson method, until function of solution is zero (simple driver)
• nag_ode_ivp_rkm_zero_simple – d02bh
• d02bj – Ordinary differential equations, initial value problem, Runge–Kutta method, until function of solution is zero, integration over range with intermediate output (simple driver)
• nag_ode_ivp_rk_zero_simple – d02bj
• d02cj – Ordinary differential equations, initial value problem, Adams method, until function of solution is zero, intermediate output (simple driver)
• nag_ode_ivp_adams_zero_simple – d02cj
• d02ej – Ordinary differential equations, stiff initial value problem, backward differentiation formulae method, until function of solution is zero, intermediate output (simple driver)
• nag_ode_ivp_bdf_zero_simple – d02ej
• d02ga – Ordinary differential equations, boundary value problem, finite difference technique with deferred correction, simple nonlinear problem
• nag_ode_bvp_fd_nonlin_fixedbc – d02ga
• d02gb – Ordinary differential equations, boundary value problem, finite difference technique with deferred correction, general linear problem
• nag_ode_bvp_fd_lin_gen – d02gb
• d02ha – Ordinary differential equations, boundary value problem, shooting and matching, boundary values to be determined
• nag_ode_bvp_shoot_bval – d02ha
• d02hb – Ordinary differential equations, boundary value problem, shooting and matching, general parameters to be determined
• nag_ode_bvp_shoot_genpar – d02hb
• d02ja – Ordinary differential equations, boundary value problem, collocation and least squares, single nth-order linear equation
• nag_ode_bvp_coll_nth – d02ja
• d02jb – Ordinary differential equations, boundary value problem, collocation and least squares, system of first-order linear equations
• nag_ode_bvp_coll_sys – d02jb
• d02ka – Second-order Sturm–Liouville problem, regular system, finite range, eigenvalue only
• nag_ode_sl2_reg_finite – d02ka
• d02kd – Second-order Sturm–Liouville problem, regular/singular system, finite/infinite range, eigenvalue only, user-specified break-points
• nag_ode_sl2_breaks_vals – d02kd
• d02ke – Second-order Sturm–Liouville problem, regular/singular system, finite/infinite range, eigenvalue and eigenfunction, user-specified break-points
• nag_ode_sl2_breaks_funs – d02ke
• d02la – Second-order ordinary differential equations, initial value problem, Runge–Kutta–Nystrom method
• nag_ode_ivp_2nd_rkn – d02la
• d02lx – Second-order ordinary differential equations, initial value problem, setup for d02la
• nag_ode_ivp_2nd_rkn_setup – d02lx
• d02ly – Second-order ordinary differential equations, initial value problem, diagnostics for d02la
• nag_ode_ivp_2nd_rkn_diag – d02ly
• d02lz – Second-order ordinary differential equations, initial value problem, interpolation for d02la
• nag_ode_ivp_2nd_rkn_interp – d02lz
• d02mc – Implicit ordinary differential equations/DAEs, initial value problem, DASSL method continuation for d02ne
• nag_ode_dae_dassl_cont – d02mc
• d02mv – Ordinary differential equations, initial value problem, DASSL method, setup for D02M–N functions
• nag_ode_ivp_stiff_dassl – d02mv
• d02mw – Implicit ordinary differential equations/DAEs, initial value problem, setup for d02ne
• nag_ode_dae_dassl_setup – d02mw
• d02mz – Ordinary differential equations, initial value problem, interpolation for D02M–N routines (all integration methods), natural interpolant
• nag_ode_ivp_stiff_interp – d02mz
• d02nb – Explicit ordinary differential equations, stiff initial value problem, full Jacobian (comprehensive)
• nag_ode_ivp_stiff_exp_fulljac – d02nb
• d02nc – Explicit ordinary differential equations, stiff initial value problem, banded Jacobian (comprehensive)
• nag_ode_ivp_stiff_exp_bandjac – d02nc
• d02nd – Explicit ordinary differential equations, stiff initial value problem, sparse Jacobian (comprehensive)
• nag_ode_ivp_stiff_exp_sparjac – d02nd
• d02ne – Implicit ordinary differential equations/DAEs, initial value problem, DASSL method integrator
• nag_ode_dae_dassl_gen – d02ne
• d02ng – Implicit/algebraic ordinary differential equations, stiff initial value problem, full Jacobian (comprehensive)
• nag_ode_ivp_stiff_imp_fulljac – d02ng
• d02nh – Implicit/algebraic ordinary differential equations, stiff initial value problem, banded Jacobian (comprehensive)
• nag_ode_ivp_stiff_imp_bandjac – d02nh
• d02nj – Implicit/algebraic ordinary differential equations, stiff initial value problem, sparse Jacobian (comprehensive)
• nag_ode_ivp_stiff_imp_sparjac – d02nj
• d02nm – Explicit ordinary differential equations, stiff initial value problem (reverse communication, comprehensive)
• nag_ode_ivp_stiff_exp_revcom – d02nm
• d02nn – Implicit/algebraic ordinary differential equations, stiff initial value problem (reverse communication, comprehensive)
• nag_ode_ivp_stiff_imp_revcom – d02nn
• d02np – Implicit ordinary differential equations/DAEs, initial value problem linear algebra setup function for d02ne
• nag_ode_dae_dassl_linalg – d02np
• d02nr – Ordinary differential equations, initial value problem, for use with D02M–N functions, sparse Jacobian, enquiry function
• nag_ode_ivp_stiff_sparjac_enq – d02nr
• d02ns – Ordinary differential equations, initial value problem, for use with D02M–N functions, full Jacobian, linear algebra set up
• nag_ode_ivp_stiff_fulljac_setup – d02ns
• d02nt – Ordinary differential equations, initial value problem, for use with D02M–N functions, banded Jacobian, linear algebra set up
• nag_ode_ivp_stiff_bandjac_setup – d02nt
• d02nu – Ordinary differential equations, initial value problem, for use with D02M–N functions, sparse Jacobian, linear algebra set up
• nag_ode_ivp_stiff_sparjac_setup – d02nu
• d02nv – Ordinary differential equations, initial value problem, backward differentiation formulae method, setup for D02M–N functions
• nag_ode_ivp_stiff_bdf – d02nv
• d02nw – Ordinary differential equations, initial value problem, Blend method, setup for D02M–N functions
• nag_ode_ivp_stiff_blend – d02nw
• d02nx – Ordinary differential equations, initial value problem, sparse Jacobian, linear algebra diagnostics, for use with D02M–N functions
• nag_ode_ivp_stiff_sparjac_diag – d02nx
• d02ny – Ordinary differential equations, initial value problem, integrator diagnostics, for use with D02M–N functions
• nag_ode_ivp_stiff_integ_diag – d02ny
• d02nz – Ordinary differential equations, initial value problem, setup for continuation calls to integrator, for use with D02M–N functions
• nag_ode_ivp_stiff_contin – d02nz
• d02pc – Ordinary differential equations, initial value problem, Runge–Kutta method, integration over range with output
• nag_ode_ivp_rk_range – d02pc
• d02pd – Ordinary differential equations, initial value problem, Runge–Kutta method, integration over one step
• nag_ode_ivp_rk_onestep – d02pd
• d02pv – Ordinary differential equations, initial value problem, setup for d02pc and d02pd
• nag_ode_ivp_rk_setup – d02pv
• d02pw – Ordinary differential equations, initial value problem, resets end of range for d02pd
• nag_ode_ivp_rk_reset_tend – d02pw
• d02px – Ordinary differential equations, initial value problem, interpolation for d02pd
• nag_ode_ivp_rk_interp – d02px
• d02py – Ordinary differential equations, initial value problem, integration diagnostics for d02pc and d02pd
• nag_ode_ivp_rk_diag – d02py
• d02pz – Ordinary differential equations, initial value problem, error assessment diagnostics for d02pc and d02pd
• nag_ode_ivp_rk_errass – d02pz
• d02qf – Ordinary differential equations, initial value problem, Adams method with root-finding (direct communication, comprehensive)
• nag_ode_ivp_adams_roots – d02qf
• d02qg – Ordinary differential equations, initial value problem, Adams method with root-finding (reverse communication, comprehensive)
• nag_ode_ivp_adams_roots_revcom – d02qg
• d02qw – Ordinary differential equations, initial value problem, setup for d02qf and d02qg
• nag_ode_ivp_adams_setup – d02qw
• d02qx – Ordinary differential equations, initial value problem, diagnostics for d02qf and d02qg
• nag_ode_ivp_adams_diag – d02qx
• d02qy – Ordinary differential equations, initial value problem, root-finding diagnostics for d02qf and d02qg
• nag_ode_ivp_adams_rootdiag – d02qy
• d02qz – Ordinary differential equations, initial value problem, interpolation for d02qf or d02qg
• nag_ode_ivp_adams_interp – d02qz
• d02ra – Ordinary differential equations, general nonlinear boundary value problem, finite difference technique with deferred correction, continuation facility
• nag_ode_bvp_fd_nonlin_gen – d02ra
• d02sa – Ordinary differential equations, boundary value problem, shooting and matching technique, subject to extra algebraic equations, general parameters to be determined
• nag_ode_bvp_shoot_genpar_algeq – d02sa
• d02tg – nth-order linear ordinary differential equations, boundary value problem, collocation and least squares
• nag_ode_bvp_coll_nth_comp – d02tg
• d02tk – Ordinary differential equations, general nonlinear boundary value problem, collocation technique
• nag_ode_bvp_coll_nlin – d02tk
• d02tv – Ordinary differential equations, general nonlinear boundary value problem, setup for d02tk
• nag_ode_bvp_coll_nlin_setup – d02tv
• d02tx – Ordinary differential equations, general nonlinear boundary value problem, continuation facility for d02tk
• nag_ode_bvp_coll_nlin_contin – d02tx
• d02ty – Ordinary differential equations, general nonlinear boundary value problem, interpolation for d02tk
• nag_ode_bvp_coll_nlin_interp – d02ty
• d02tz – Ordinary differential equations, general nonlinear boundary value problem, diagnostics for d02tk
• nag_ode_bvp_coll_nlin_diag – d02tz
• d02ua – Coefficients of Chebyshev interpolating polynomial from function values on Chebyshev grid
• nag_ode_bvp_ps_lin_coeffs – d02ua
• d02ub – Function or low-order-derivative values on Chebyshev grid from coefficients of Chebyshev interpolating polynomial
• nag_ode_bvp_ps_lin_cgl_vals – d02ub
• d02uc – Chebyshev Gauss–Lobatto grid generation
• nag_ode_bvp_ps_lin_cgl_grid – d02uc
• d02ud – Differentiate a function by the FFT using function values on Chebyshev grid
• nag_ode_bvp_ps_lin_cgl_deriv – d02ud
• d02ue – Solve linear constant coefficient boundary value problem on Chebyshev grid, Integral formulation
• nag_ode_bvp_ps_lin_solve – d02ue
• d02uw – Interpolate a function from Chebyshev grid to uniform grid using barycentric Lagrange interpolation
• nag_ode_bvp_ps_lin_grid_vals – d02uw
• d02uy – Clenshaw–Curtis quadrature weights for integration using computed Chebyshev coefficients
• nag_ode_bvp_ps_lin_quad_weights – d02uy
• d02uz – Chebyshev polynomial evaluation, T_k(x)
• nag_ode_bvp_ps_lin_cheb_eval – d02uz
• d02xj – Ordinary differential equations, initial value problem, interpolation for D02M–N routines (BLEND and BDF methods only), natural interpolant
• nag_ode_ivp_stiff_nat_interp – d02xj
• d02xk – Ordinary differential equations, initial value problem, interpolation for D02M–N functions, C^1 interpolant
• nag_ode_ivp_stiff_c1_interp – d02xk
• d02za – Ordinary differential equations, initial value problem, weighted norm of local error estimate for D02M–N functions
• nag_ode_ivp_stiff_errest – d02za
 D01 D03