# NAG FL InterfaceD02 (Ode)Ordinary Differential Equations

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
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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
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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
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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
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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
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Ordinary differential equations, initial value problem, Adams' method, until function of solution is zero, intermediate output (simple driver)
d02ejf
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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
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8 nagf_ode_bvp_fd_nonlin_fixedbc
Ordinary differential equations, boundary value problem, finite difference technique with deferred correction, simple nonlinear problem
d02gbf
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8 nagf_ode_bvp_fd_lin_gen
Ordinary differential equations, boundary value problem, finite difference technique with deferred correction, general linear problem
d02haf
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8 nagf_ode_bvp_shoot_bval
Ordinary differential equations, boundary value problem, shooting and matching, boundary values to be determined
d02hbf
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8 nagf_ode_bvp_shoot_genpar
Ordinary differential equations, boundary value problem, shooting and matching, general parameters to be determined
d02jaf
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8 nagf_ode_bvp_coll_nth
Ordinary differential equations, boundary value problem, collocation and least squares, single $n$th-order linear equation
d02jbf
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8 nagf_ode_bvp_coll_sys
Ordinary differential equations, boundary value problem, collocation and least squares, system of first-order linear equations
d02kaf
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7 nagf_ode_sl2_reg_finite
Second-order Sturm–Liouville problem, regular system, finite range, eigenvalue only
d02kdf
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7 nagf_ode_sl2_breaks_vals
Second-order Sturm–Liouville problem, regular/singular system, finite/infinite range, eigenvalue only, user-specified break-points
d02kef
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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
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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
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14 nagf_ode_ivp_stiff_dassl
Ordinary differential equations, initial value problem, DASSL method, setup for d02m–n routines
d02mwf
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22 nagf_ode_dae_dassl_setup
Implicit ordinary differential equations/DAEs, initial value problem, setup for d02nef
d02mzf
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14 nagf_ode_ivp_stiff_interp
Ordinary differential equations, initial value problem, interpolation for d02m–n routines (all integration methods), natural interpolant
d02nbf
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12 nagf_ode_ivp_stiff_exp_fulljac
Explicit ordinary differential equations, stiff initial value problem, full Jacobian (comprehensive)
d02ncf
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12 nagf_ode_ivp_stiff_exp_bandjac
Explicit ordinary differential equations, stiff initial value problem, banded Jacobian (comprehensive)
d02ndf
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12 nagf_ode_ivp_stiff_exp_sparjac
Explicit ordinary differential equations, stiff initial value problem, sparse Jacobian (comprehensive)
d02nef
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22 nagf_ode_dae_dassl_gen
Implicit ordinary differential equations/DAEs, initial value problem, DASSL method integrator
d02ngf
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12 nagf_ode_ivp_stiff_imp_fulljac
Implicit/algebraic ordinary differential equations, stiff initial value problem, full Jacobian (comprehensive)
d02nhf
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12 nagf_ode_ivp_stiff_imp_bandjac
Implicit/algebraic ordinary differential equations, stiff initial value problem, banded Jacobian (comprehensive)
d02njf
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12 nagf_ode_ivp_stiff_imp_sparjac
Implicit/algebraic ordinary differential equations, stiff initial value problem, sparse Jacobian (comprehensive)
d02nmf
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12 nagf_ode_ivp_stiff_exp_revcom
Explicit ordinary differential equations, stiff initial value problem (reverse communication, comprehensive)
d02nnf
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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
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24 nagf_ode_ivp_rkts_range
Ordinary differential equations, initial value problem, Runge–Kutta method, integration over range with output
d02pff
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24 nagf_ode_ivp_rkts_onestep
Ordinary differential equations, initial value problem, Runge–Kutta method, integration over one step
d02pgf
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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
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24 nagf_ode_ivp_rkts_reset_tend
Ordinary differential equations, initial value problem, resets end of range for d02pff
d02psf
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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
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24 nagf_ode_ivp_rkts_errass
Ordinary differential equations, initial value problem, error assessment diagnostics for d02pef and d02pff
d02qff
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Ordinary differential equations, initial value problem, Adams' method with root-finding (direct communication, comprehensive)
d02qgf
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Ordinary differential equations, initial value problem, Adams' method with root-finding (reverse communication, comprehensive)
Ordinary differential equations, initial value problem, setup for d02qff and d02qgf
Ordinary differential equations, initial value problem, diagnostics for d02qff and d02qgf
Ordinary differential equations, initial value problem, root-finding diagnostics for d02qff and d02qgf
d02qzf
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Ordinary differential equations, initial value problem, interpolation for d02qff or d02qgf
d02raf
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8 nagf_ode_bvp_fd_nonlin_gen
Ordinary differential equations, general nonlinear boundary value problem, finite difference technique with deferred correction, continuation facility
d02saf
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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
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8 nagf_ode_bvp_coll_nth_comp
$n$th-order linear ordinary differential equations, boundary value problem, collocation and least squares
d02tlf
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25 nagf_ode_bvp_coll_nlin_solve
Ordinary differential equations, general nonlinear boundary value problem, collocation technique (thread safe)
d02tvf
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17 nagf_ode_bvp_coll_nlin_setup
Ordinary differential equations, general nonlinear boundary value problem, setup for d02tlf
d02txf
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17 nagf_ode_bvp_coll_nlin_contin
Ordinary differential equations, general nonlinear boundary value problem, continuation facility for d02tlf
d02tyf
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17 nagf_ode_bvp_coll_nlin_interp
Ordinary differential equations, general nonlinear boundary value problem, interpolation for d02tlf
d02tzf
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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
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23 nagf_ode_bvp_ps_lin_cgl_deriv
Differentiate a function by the FFT using function values on Chebyshev grid
d02uef
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23 nagf_ode_bvp_ps_lin_solve
Solve linear constant coefficient boundary value problem on Chebyshev grid, Integral formulation
d02uwf
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23 nagf_ode_bvp_ps_lin_grid_vals
Interpolate a function from Chebyshev grid to uniform grid using barycentric Lagrange interpolation
d02uyf
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Clenshaw–Curtis quadrature weights for integration using computed Chebyshev coefficients
d02uzf
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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
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12 nagf_ode_ivp_stiff_errest
Ordinary differential equations, initial value problem, weighted norm of local error estimate for d02m–n routines