# NAG FL InterfaceD02 (Ode)Ordinary Differential Equations

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D02 (Ode) Chapter Introduction – A description of the Chapter and an overview of the algorithms available.
D02M–N Sub-chapter Introduction

Routine
Mark of
Introduction

Purpose
d02agf 2 nagf_ode_bvp_shoot_genpar_intern
Ordinary differential equations, boundary value problem, shooting and matching technique, allowing interior matching point, general parameters to be determined
d02bgf 7 nagf_ode_ivp_rkm_val_simple
Ordinary differential equations, initial value problem, Runge–Kutta–Merson method, until a component attains given value (simple driver)
d02bhf 7 nagf_ode_ivp_rkm_zero_simple
Ordinary differential equations, initial value problem, Runge–Kutta–Merson method, until function of solution is zero (simple driver)
d02bjf 18 nagf_ode_ivp_rk_zero_simple
Ordinary differential equations, initial value problem, Runge–Kutta method, until function of solution is zero, integration over range with intermediate output (simple driver)
d02cjf 13 nagf_ode_ivp_adams_zero_simple
Ordinary differential equations, initial value problem, Adams' method, until function of solution is zero, intermediate output (simple driver)
d02ejf 12 nagf_ode_ivp_bdf_zero_simple
Ordinary differential equations, stiff initial value problem, backward differentiation formulae method, until function of solution is zero, intermediate output (simple driver)
d02gaf 8 nagf_ode_bvp_fd_nonlin_fixedbc
Ordinary differential equations, boundary value problem, finite difference technique with deferred correction, simple nonlinear problem
d02gbf 8 nagf_ode_bvp_fd_lin_gen
Ordinary differential equations, boundary value problem, finite difference technique with deferred correction, general linear problem
d02haf 8 nagf_ode_bvp_shoot_bval
Ordinary differential equations, boundary value problem, shooting and matching, boundary values to be determined
d02hbf 8 nagf_ode_bvp_shoot_genpar
Ordinary differential equations, boundary value problem, shooting and matching, general parameters to be determined
d02jaf 8 nagf_ode_bvp_coll_nth
Ordinary differential equations, boundary value problem, collocation and least squares, single $n$th-order linear equation
d02jbf 8 nagf_ode_bvp_coll_sys
Ordinary differential equations, boundary value problem, collocation and least squares, system of first-order linear equations
d02kaf 7 nagf_ode_sl2_reg_finite
Second-order Sturm–Liouville problem, regular system, finite range, eigenvalue only
d02kdf 7 nagf_ode_sl2_breaks_vals
Second-order Sturm–Liouville problem, regular/singular system, finite/infinite range, eigenvalue only, user-specified break-points
d02kef 8 nagf_ode_sl2_breaks_funs
Second-order Sturm–Liouville problem, regular/singular system, finite/infinite range, eigenvalue and eigenfunction, user-specified break-points
d02laf 13 nagf_ode_ivp_2nd_rkn
Second-order ordinary differential equations, initial value problem, Runge–Kutta–Nystrom method
d02lxf 13 nagf_ode_ivp_2nd_rkn_setup
Second-order ordinary differential equations, initial value problem, setup for d02laf
d02lyf 13 nagf_ode_ivp_2nd_rkn_diag
Second-order ordinary differential equations, initial value problem, diagnostics for d02laf
d02lzf 13 nagf_ode_ivp_2nd_rkn_interp
Second-order ordinary differential equations, initial value problem, interpolation for d02laf
d02mcf 22 nagf_ode_dae_dassl_cont
Implicit ordinary differential equations/DAEs, initial value problem, DASSL method continuation for d02nef
d02mvf 14 nagf_ode_ivp_stiff_dassl
Ordinary differential equations, initial value problem, DASSL method, setup for d02m–n routines
d02mwf 22 nagf_ode_dae_dassl_setup
Implicit ordinary differential equations/DAEs, initial value problem, setup for d02nef
d02mzf 14 nagf_ode_ivp_stiff_interp
Ordinary differential equations, initial value problem, interpolation for d02m–n routines (all integration methods), natural interpolant
d02nbf 12 nagf_ode_ivp_stiff_exp_fulljac
Explicit ordinary differential equations, stiff initial value problem, full Jacobian (comprehensive)
d02ncf 12 nagf_ode_ivp_stiff_exp_bandjac
Explicit ordinary differential equations, stiff initial value problem, banded Jacobian (comprehensive)
d02ndf 12 nagf_ode_ivp_stiff_exp_sparjac
Explicit ordinary differential equations, stiff initial value problem, sparse Jacobian (comprehensive)
d02nef 22 nagf_ode_dae_dassl_gen
Implicit ordinary differential equations/DAEs, initial value problem, DASSL method integrator
d02ngf 12 nagf_ode_ivp_stiff_imp_fulljac
Implicit/algebraic ordinary differential equations, stiff initial value problem, full Jacobian (comprehensive)
d02nhf 12 nagf_ode_ivp_stiff_imp_bandjac
Implicit/algebraic ordinary differential equations, stiff initial value problem, banded Jacobian (comprehensive)
d02njf 12 nagf_ode_ivp_stiff_imp_sparjac
Implicit/algebraic ordinary differential equations, stiff initial value problem, sparse Jacobian (comprehensive)
d02nmf 12 nagf_ode_ivp_stiff_exp_revcom
Explicit ordinary differential equations, stiff initial value problem (reverse communication, comprehensive)
d02nnf 12 nagf_ode_ivp_stiff_imp_revcom
Implicit/algebraic ordinary differential equations, stiff initial value problem (reverse communication, comprehensive)
d02npf 22 nagf_ode_dae_dassl_linalg
Implicit ordinary differential equations/DAEs, initial value problem linear algebra setup routine for d02nef
d02nrf 12 nagf_ode_ivp_stiff_sparjac_enq
Ordinary differential equations, initial value problem, for use with d02m–n routines, sparse Jacobian, enquiry routine
d02nsf 12 nagf_ode_ivp_stiff_fulljac_setup
Ordinary differential equations, initial value problem, for use with d02m–n routines, full Jacobian, linear algebra set up
d02ntf 12 nagf_ode_ivp_stiff_bandjac_setup
Ordinary differential equations, initial value problem, for use with d02m–n routines, banded Jacobian, linear algebra set up
d02nuf 12 nagf_ode_ivp_stiff_sparjac_setup
Ordinary differential equations, initial value problem, for use with d02m–n routines, sparse Jacobian, linear algebra set up
d02nvf 12 nagf_ode_ivp_stiff_bdf
Ordinary differential equations, initial value problem, backward differentiation formulae method, setup for d02m–n routines
d02nwf 12 nagf_ode_ivp_stiff_blend
Ordinary differential equations, initial value problem, Blend method, setup for d02m–n routines
d02nxf 12 nagf_ode_ivp_stiff_sparjac_diag
Ordinary differential equations, initial value problem, sparse Jacobian, linear algebra diagnostics, for use with d02m–n routines
d02nyf 12 nagf_ode_ivp_stiff_integ_diag
Ordinary differential equations, initial value problem, integrator diagnostics, for use with d02m–n routines
d02nzf 12 nagf_ode_ivp_stiff_contin
Ordinary differential equations, initial value problem, setup for continuation calls to integrator, for use with d02m–n routines
d02pef 24 nagf_ode_ivp_rkts_range
Ordinary differential equations, initial value problem, Runge–Kutta method, integration over range with output
d02pff 24 nagf_ode_ivp_rkts_onestep
Ordinary differential equations, initial value problem, Runge–Kutta method, integration over one step
d02pgf 26 nagf_ode_ivp_rk_step_revcomm
Ordinary differential equations, initial value problem, Runge–Kutta method, integration by reverse communication
d02phf 26 nagf_ode_ivp_rk_interp_setup
Set up interpolant by reverse communication for solution and derivative evaluations at points within the range of the last integration step taken by d02pgf
d02pjf 26 nagf_ode_ivp_rk_interp_eval
Evaluate interpolant, set up using d02pqf, to approximate solution and/or solution derivatives at a point within the range of the last integration step taken by d02pgf
d02pqf 24 nagf_ode_ivp_rkts_setup
Ordinary differential equations, initial value problem, setup for d02pef and d02pff
d02prf 24 nagf_ode_ivp_rkts_reset_tend
Ordinary differential equations, initial value problem, resets end of range for d02pff
d02psf 24 nagf_ode_ivp_rkts_interp
Ordinary differential equations, initial value problem, interpolation for d02pff
d02ptf 24 nagf_ode_ivp_rkts_diag
Ordinary differential equations, initial value problem, integration diagnostics for d02pef and d02pff
d02puf 24 nagf_ode_ivp_rkts_errass
Ordinary differential equations, initial value problem, error assessment diagnostics for d02pef and d02pff
d02qff 13 nagf_ode_ivp_adams_roots
Ordinary differential equations, initial value problem, Adams' method with root-finding (direct communication, comprehensive)
d02qgf 13 nagf_ode_ivp_adams_roots_revcom
Ordinary differential equations, initial value problem, Adams' method with root-finding (reverse communication, comprehensive)
d02qwf 13 nagf_ode_ivp_adams_setup
Ordinary differential equations, initial value problem, setup for d02qff and d02qgf
d02qxf 13 nagf_ode_ivp_adams_diag
Ordinary differential equations, initial value problem, diagnostics for d02qff and d02qgf
d02qyf 13 nagf_ode_ivp_adams_rootdiag
Ordinary differential equations, initial value problem, root-finding diagnostics for d02qff and d02qgf
d02qzf 13 nagf_ode_ivp_adams_interp
Ordinary differential equations, initial value problem, interpolation for d02qff or d02qgf
d02raf 8 nagf_ode_bvp_fd_nonlin_gen
Ordinary differential equations, general nonlinear boundary value problem, finite difference technique with deferred correction, continuation facility
d02saf 8 nagf_ode_bvp_shoot_genpar_algeq
Ordinary differential equations, boundary value problem, shooting and matching technique, subject to extra algebraic equations, general parameters to be determined
d02tgf 8 nagf_ode_bvp_coll_nth_comp
$n$th-order linear ordinary differential equations, boundary value problem, collocation and least squares
d02tlf 25 nagf_ode_bvp_coll_nlin_solve
Ordinary differential equations, general nonlinear boundary value problem, collocation technique (thread safe)
d02tvf 17 nagf_ode_bvp_coll_nlin_setup
Ordinary differential equations, general nonlinear boundary value problem, setup for d02tlf
d02txf 17 nagf_ode_bvp_coll_nlin_contin
Ordinary differential equations, general nonlinear boundary value problem, continuation facility for d02tlf
d02tyf 17 nagf_ode_bvp_coll_nlin_interp
Ordinary differential equations, general nonlinear boundary value problem, interpolation for d02tlf
d02tzf 17 nagf_ode_bvp_coll_nlin_diag
Ordinary differential equations, general nonlinear boundary value problem, diagnostics for d02tlf
d02uaf 23 nagf_ode_bvp_ps_lin_coeffs
Coefficients of Chebyshev interpolating polynomial from function values on Chebyshev grid
d02ubf 23 nagf_ode_bvp_ps_lin_cgl_vals
Function or low-order-derivative values on Chebyshev grid from coefficients of Chebyshev interpolating polynomial
d02ucf 23 nagf_ode_bvp_ps_lin_cgl_grid
Chebyshev Gauss–Lobatto grid generation
d02udf 23 nagf_ode_bvp_ps_lin_cgl_deriv
Differentiate a function by the FFT using function values on Chebyshev grid
d02uef 23 nagf_ode_bvp_ps_lin_solve
Solve linear constant coefficient boundary value problem on Chebyshev grid, Integral formulation
d02uwf 23 nagf_ode_bvp_ps_lin_grid_vals
Interpolate a function from Chebyshev grid to uniform grid using barycentric Lagrange interpolation
d02uyf 23 nagf_ode_bvp_ps_lin_quad_weights
Clenshaw–Curtis quadrature weights for integration using computed Chebyshev coefficients
d02uzf 23 nagf_ode_bvp_ps_lin_cheb_eval
Chebyshev polynomial evaluation, ${T}_{k}\left(x\right)$
d02xjf 12 nagf_ode_ivp_stiff_nat_interp
Ordinary differential equations, initial value problem, interpolation for d02m–n routines (BLEND and BDF methods only), natural interpolant
d02xkf 12 nagf_ode_ivp_stiff_c1_interp
Ordinary differential equations, initial value problem, interpolation for d02m–n routines, ${C}^{1}$ interpolant
d02zaf 12 nagf_ode_ivp_stiff_errest
Ordinary differential equations, initial value problem, weighted norm of local error estimate for d02m–n routines