# NAG Library Chapter Contents

## D02 (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

 RoutineName Mark ofIntroduction Purpose d02agf Example Text Example DataExample Plot 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 Example Text Example Data 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 Example Text Example Data 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 Example Text Example DataExample Plot 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 Example Text Example DataExample Plot 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 Example Text Example DataExample Plot 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 Example Text Example DataExample Plot 8 nagf_ode_bvp_fd_nonlin_fixedbc Ordinary differential equations, boundary value problem, finite difference technique with deferred correction, simple nonlinear problem d02gbf Example Text Example DataExample Plot 8 nagf_ode_bvp_fd_lin_gen Ordinary differential equations, boundary value problem, finite difference technique with deferred correction, general linear problem d02haf Example Text Example DataExample Plot 8 nagf_ode_bvp_shoot_bval Ordinary differential equations, boundary value problem, shooting and matching, boundary values to be determined d02hbf Example Text Example DataExample Plot 8 nagf_ode_bvp_shoot_genpar Ordinary differential equations, boundary value problem, shooting and matching, general parameters to be determined d02jaf Example Text Example DataExample Plot 8 nagf_ode_bvp_coll_nth Ordinary differential equations, boundary value problem, collocation and least squares, single $n$th-order linear equation d02jbf Example Text Example DataExample Plot 8 nagf_ode_bvp_coll_sys Ordinary differential equations, boundary value problem, collocation and least squares, system of first-order linear equations d02kaf Example Text Example Data 7 nagf_ode_sl2_reg_finite Second-order Sturm–Liouville problem, regular system, finite range, eigenvalue only d02kdf Example Text Example Data 7 nagf_ode_sl2_breaks_vals Second-order Sturm–Liouville problem, regular/singular system, finite/infinite range, eigenvalue only, user-specified break-points d02kef Example Text Example DataExample Plot 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 Example Text Example DataExample Plot 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 Example Text Example DataExample Plot 14 nagf_ode_ivp_stiff_dassl Ordinary differential equations, initial value problem, DASSL method, setup for d02m–n routines d02mwf Example Text Example Data 22 nagf_ode_dae_dassl_setup Implicit ordinary differential equations/DAEs, initial value problem, setup for d02nef d02mzf Example Text Example Data 14 nagf_ode_ivp_stiff_interp Ordinary differential equations, initial value problem, interpolation for d02m–n routines (all integration methods), natural interpolant d02nbf Example Text Example DataExample Plot 12 nagf_ode_ivp_stiff_exp_fulljac Explicit ordinary differential equations, stiff initial value problem, full Jacobian (comprehensive) d02ncf Example Text Example DataExample Plot 12 nagf_ode_ivp_stiff_exp_bandjac Explicit ordinary differential equations, stiff initial value problem, banded Jacobian (comprehensive) d02ndf Example Text Example DataExample Plot 12 nagf_ode_ivp_stiff_exp_sparjac Explicit ordinary differential equations, stiff initial value problem, sparse Jacobian (comprehensive) d02nef Example Text Example Data 22 nagf_ode_dae_dassl_gen Implicit ordinary differential equations/DAEs, initial value problem, DASSL method integrator d02ngf Example Text Example DataExample Plot 12 nagf_ode_ivp_stiff_imp_fulljac Implicit/algebraic ordinary differential equations, stiff initial value problem, full Jacobian (comprehensive) d02nhf Example Text Example Data 12 nagf_ode_ivp_stiff_imp_bandjac Implicit/algebraic ordinary differential equations, stiff initial value problem, banded Jacobian (comprehensive) d02njf Example Text Example DataExample Plot 12 nagf_ode_ivp_stiff_imp_sparjac Implicit/algebraic ordinary differential equations, stiff initial value problem, sparse Jacobian (comprehensive) d02nmf Example Text Example DataExample Plot 12 nagf_ode_ivp_stiff_exp_revcom Explicit ordinary differential equations, stiff initial value problem (reverse communication, comprehensive) d02nnf Example Text Example Data 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 Example Text Example DataExample Plot 24 nagf_ode_ivp_rkts_range Ordinary differential equations, initial value problem, Runge–Kutta method, integration over range with output d02pff Example Text Example DataExample Plot 24 nagf_ode_ivp_rkts_onestep Ordinary differential equations, initial value problem, Runge–Kutta method, integration over one step d02pgf Example Text Example DataExample Plot 26.0 nagf_ode_ivp_rk_step_revcomm Ordinary differential equations, initial value problem, Runge–Kutta method, integration by reverse communication d02phf 26.0 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 26.0 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 Example Text Example DataExample Plot 24 nagf_ode_ivp_rkts_reset_tend Ordinary differential equations, initial value problem, resets end of range for d02pff d02psf Example Text Example DataExample Plot 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 Example Text Example DataExample Plot 24 nagf_ode_ivp_rkts_errass Ordinary differential equations, initial value problem, error assessment diagnostics for d02pef and d02pff d02qff Example Text Example Data 13 nagf_ode_ivp_adams_roots Ordinary differential equations, initial value problem, Adams' method with root-finding (direct communication, comprehensive) d02qgf Example Text Example DataExample Plot 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 Example Text Example DataExample Plot 13 nagf_ode_ivp_adams_interp Ordinary differential equations, initial value problem, interpolation for d02qff or d02qgf d02raf Example Text Example DataExample Plot 8 nagf_ode_bvp_fd_nonlin_gen Ordinary differential equations, general nonlinear boundary value problem, finite difference technique with deferred correction, continuation facility d02saf Example Text Example DataExample Plot 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 Example Text Example DataExample Plot 8 nagf_ode_bvp_coll_nth_comp $n$th-order linear ordinary differential equations, boundary value problem, collocation and least squares d02tkf Example Text Example DataExample Plot 17 nagf_ode_withdraw_bvp_coll_nlin Ordinary differential equations, general nonlinear boundary value problem, collocation techniqueNote: this routine is scheduled for withdrawal at Mark 27, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information. d02tlf Example Text Example DataExample Plot 25 nagf_ode_bvp_coll_nlin_solve Ordinary differential equations, general nonlinear boundary value problem, collocation technique (thread safe) d02tvf Example Text Example DataExample Plot 17 nagf_ode_bvp_coll_nlin_setup Ordinary differential equations, general nonlinear boundary value problem, setup for d02tlf d02txf Example Text Example DataExample Plot 17 nagf_ode_bvp_coll_nlin_contin Ordinary differential equations, general nonlinear boundary value problem, continuation facility for d02tlf d02tyf Example Text Example DataExample Plot 17 nagf_ode_bvp_coll_nlin_interp Ordinary differential equations, general nonlinear boundary value problem, interpolation for d02tlf d02tzf Example Text Example DataExample Plot 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 Example Text Example Data 23 nagf_ode_bvp_ps_lin_cgl_deriv Differentiate a function by the FFT using function values on Chebyshev grid d02uef Example Text Example Data 23 nagf_ode_bvp_ps_lin_solve Solve linear constant coefficient boundary value problem on Chebyshev grid, Integral formulation d02uwf Example Text Example Data 23 nagf_ode_bvp_ps_lin_grid_vals Interpolate a function from Chebyshev grid to uniform grid using barycentric Lagrange interpolation d02uyf Example Text Example Data 23 nagf_ode_bvp_ps_lin_quad_weights Clenshaw–Curtis quadrature weights for integration using computed Chebyshev coefficients d02uzf Example Text Example Data 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 Example Text Example Data 12 nagf_ode_ivp_stiff_errest Ordinary differential equations, initial value problem, weighted norm of local error estimate for d02m–n routines