D02 Chapter Contents (PDF version)
D02 Chapter Introduction
NAG Library Manual

NAG Library Chapter Contents

D02 – Ordinary Differential Equations

D02 Chapter Introduction
D02M–N Sub-chapter Introduction

Routine
Name
Mark of
Introduction

Purpose
D02AGF
Example Text
Example Data
Example 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 Data
Example 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 Data
Example 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 Data
Example 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 Data
Example 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 Data
Example 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 Data
Example 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 Data
Example 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 Data
Example Plot
8 nagf_ode_bvp_coll_nth
Ordinary differential equations, boundary value problem, collocation and least squares, single nth-order linear equation
D02JBF
Example Text
Example Data
Example 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 Data
Example 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 Data
Example 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 Data
Example 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 Data
Example Plot
12 nagf_ode_ivp_stiff_exp_fulljac
Explicit ordinary differential equations, stiff initial value problem, full Jacobian (comprehensive)
D02NCF
Example Text
Example Data
Example Plot
12 nagf_ode_ivp_stiff_exp_bandjac
Explicit ordinary differential equations, stiff initial value problem, banded Jacobian (comprehensive)
D02NDF
Example Text
Example Data
Example 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 Data
Example 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 Data
Example Plot
12 nagf_ode_ivp_stiff_imp_sparjac
Implicit/algebraic ordinary differential equations, stiff initial value problem, sparse Jacobian (comprehensive)
D02NMF
Example Text
Example Data
Example 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
D02PCF
Example Text
Example Data
Example Plot
16 nagf_ode_ivp_rk_range
Ordinary differential equations, initial value problem, Runge–Kutta method, integration over range with output
D02PDF
Example Text
Example Data
Example Plot
16 nagf_ode_ivp_rk_onestep
Ordinary differential equations, initial value problem, Runge–Kutta method, integration over one step
D02PVF 16 nagf_ode_ivp_rk_setup
Ordinary differential equations, initial value problem, setup for D02PCF and D02PDF
D02PWF
Example Text
Example Data
Example Plot
16 nagf_ode_ivp_rk_reset_tend
Ordinary differential equations, initial value problem, resets end of range for D02PDF
D02PXF
Example Text
Example Data
Example Plot
16 nagf_ode_ivp_rk_interp
Ordinary differential equations, initial value problem, interpolation for D02PDF
D02PYF 16 nagf_ode_ivp_rk_diag
Ordinary differential equations, initial value problem, integration diagnostics for D02PCF and D02PDF
D02PZF
Example Text
Example Data
Example Plot
16 nagf_ode_ivp_rk_errass
Ordinary differential equations, initial value problem, error assessment diagnostics for D02PCF and D02PDF
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 Data
Example 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 Data
Example Plot
13 nagf_ode_ivp_adams_interp
Ordinary differential equations, initial value problem, interpolation for D02QFF or D02QGF
D02RAF
Example Text
Example Data
Example 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 Data
Example 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 Data
Example Plot
8 nagf_ode_bvp_coll_nth_comp
nth-order linear ordinary differential equations, boundary value problem, collocation and least squares
D02TKF
Example Text
Example Data
Example Plot
17 nagf_ode_bvp_coll_nlin
Ordinary differential equations, general nonlinear boundary value problem, collocation technique
D02TVF
Example Text
Example Data
Example Plot
17 nagf_ode_bvp_coll_nlin_setup
Ordinary differential equations, general nonlinear boundary value problem, setup for D02TKF
D02TXF
Example Text
Example Data
Example Plot
17 nagf_ode_bvp_coll_nlin_contin
Ordinary differential equations, general nonlinear boundary value problem, continuation facility for D02TKF
D02TYF
Example Text
Example Data
Example Plot
17 nagf_ode_bvp_coll_nlin_interp
Ordinary differential equations, general nonlinear boundary value problem, interpolation for D02TKF
D02TZF
Example Text
Example Data
Example Plot
17 nagf_ode_bvp_coll_nlin_diag
Ordinary differential equations, general nonlinear boundary value problem, diagnostics for D02TKF
D02UAF
Example Text
Example Data
23 nagf_ode_bvp_ps_lin_coeffs
Coefficients of Chebyshev interpolating polynomial from function values on Chebyshev grid
D02UBF
Example Text
Example Data
23 nagf_ode_bvp_ps_lin_cgl_vals
Function or low-order-derivative values on Chebyshev grid from coefficients of Chebyshev interpolating polynomial
D02UCF
Example Text
Example Data
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, Tk(x)
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, C1 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

D02 Chapter Contents (PDF version)
D02 Chapter Introduction
NAG Library Manual

© The Numerical Algorithms Group Ltd, Oxford, UK. 2011