NAG Toolbox

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
• 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
• 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
• 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
• 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
• 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
• d02ga – Ordinary differential equations, boundary value problem, finite difference technique with deferred correction, simple nonlinear problem
• nag_ode_bvp_fd_nonlin_fixedbc
• d02gb – Ordinary differential equations, boundary value problem, finite difference technique with deferred correction, general linear problem
• nag_ode_bvp_fd_lin_gen
• d02ha – Ordinary differential equations, boundary value problem, shooting and matching, boundary values to be determined
• nag_ode_bvp_shoot_bval
• d02hb – Ordinary differential equations, boundary value problem, shooting and matching, general parameters to be determined
• nag_ode_bvp_shoot_genpar
• d02ja – Ordinary differential equations, boundary value problem, collocation and least squares, single nth-order linear equation
• nag_ode_bvp_coll_nth
• d02jb – Ordinary differential equations, boundary value problem, collocation and least squares, system of first-order linear equations
• nag_ode_bvp_coll_sys
• d02ka – Second-order Sturm–Liouville problem, regular system, finite range, eigenvalue only
• nag_ode_sl2_reg_finite
• d02kd – Second-order Sturm–Liouville problem, regular/singular system, finite/infinite range, eigenvalue only, user-specified break-points
• nag_ode_sl2_breaks_vals
• d02ke – Second-order Sturm–Liouville problem, regular/singular system, finite/infinite range, eigenvalue and eigenfunction, user-specified break-points
• nag_ode_sl2_breaks_funs
• d02la – Second-order ordinary differential equations, initial value problem, Runge–Kutta–Nystrom method
• nag_ode_ivp_2nd_rkn
• d02lx – Second-order ordinary differential equations, initial value problem, setup for d02la
• nag_ode_ivp_2nd_rkn_setup
• d02ly – Second-order ordinary differential equations, initial value problem, diagnostics for d02la
• nag_ode_ivp_2nd_rkn_diag
• d02lz – Second-order ordinary differential equations, initial value problem, interpolation for d02la
• nag_ode_ivp_2nd_rkn_interp
• d02mc – Implicit ordinary differential equations/DAEs, initial value problem, DASSL method continuation for d02ne
• nag_ode_dae_dassl_cont
• d02mv – Ordinary differential equations, initial value problem, DASSL method, setup for D02M–N functions
• nag_ode_ivp_stiff_dassl
• d02mw – Implicit ordinary differential equations/DAEs, initial value problem, setup for d02ne
• nag_ode_dae_dassl_setup
• d02mz – Ordinary differential equations, initial value problem, interpolation for D02M–N routines (all integration methods), natural interpolant
• nag_ode_ivp_stiff_interp
• d02nb – Explicit ordinary differential equations, stiff initial value problem, full Jacobian (comprehensive)
• nag_ode_ivp_stiff_exp_fulljac
• d02nc – Explicit ordinary differential equations, stiff initial value problem, banded Jacobian (comprehensive)
• nag_ode_ivp_stiff_exp_bandjac
• d02nd – Explicit ordinary differential equations, stiff initial value problem, sparse Jacobian (comprehensive)
• nag_ode_ivp_stiff_exp_sparjac
• d02ne – Implicit ordinary differential equations/DAEs, initial value problem, DASSL method integrator
• nag_ode_dae_dassl_gen
• d02ng – Implicit/algebraic ordinary differential equations, stiff initial value problem, full Jacobian (comprehensive)
• nag_ode_ivp_stiff_imp_fulljac
• d02nh – Implicit/algebraic ordinary differential equations, stiff initial value problem, banded Jacobian (comprehensive)
• nag_ode_ivp_stiff_imp_bandjac
• d02nj – Implicit/algebraic ordinary differential equations, stiff initial value problem, sparse Jacobian (comprehensive)
• nag_ode_ivp_stiff_imp_sparjac
• d02nm – Explicit ordinary differential equations, stiff initial value problem (reverse communication, comprehensive)
• nag_ode_ivp_stiff_exp_revcom
• d02nn – Implicit/algebraic ordinary differential equations, stiff initial value problem (reverse communication, comprehensive)
• nag_ode_ivp_stiff_imp_revcom
• d02np – Implicit ordinary differential equations/DAEs, initial value problem linear algebra setup function for d02ne
• nag_ode_dae_dassl_linalg
• d02nr – Ordinary differential equations, initial value problem, for use with D02M–N functions, sparse Jacobian, enquiry function
• nag_ode_ivp_stiff_sparjac_enq
• 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
• 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
• 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
• d02nv – Ordinary differential equations, initial value problem, backward differentiation formulae method, setup for D02M–N functions
• nag_ode_ivp_stiff_bdf
• d02nw – Ordinary differential equations, initial value problem, Blend method, setup for D02M–N functions
• nag_ode_ivp_stiff_blend
• d02nx – Ordinary differential equations, initial value problem, sparse Jacobian, linear algebra diagnostics, for use with D02M–N functions
• nag_ode_ivp_stiff_sparjac_diag
• d02ny – Ordinary differential equations, initial value problem, integrator diagnostics, for use with D02M–N functions
• nag_ode_ivp_stiff_integ_diag
• d02nz – Ordinary differential equations, initial value problem, setup for continuation calls to integrator, for use with D02M–N functions
• nag_ode_ivp_stiff_contin
• d02pe – Ordinary differential equations, initial value problem, Runge–Kutta method, integration over range with output
• nag_ode_ivp_rkts_range
• d02pf – Ordinary differential equations, initial value problem, Runge–Kutta method, integration over one step
• nag_ode_ivp_rkts_onestep
• d02pq – Ordinary differential equations, initial value problem, setup for d02pe, d02pf
• nag_ode_ivp_rkts_setup
• d02pr – Ordinary differential equations, initial value problem, resets end of range for d02pf
• nag_ode_ivp_rkts_reset_tend
• d02ps – Ordinary differential equations, initial value problem, interpolation for d02pf
• nag_ode_ivp_rkts_interp
• d02pt – Ordinary differential equations, initial value problem, integration diagnostics for d02pe, d02pf
• nag_ode_ivp_rkts_diag
• d02pu – Ordinary differential equations, initial value problem, error assessment diagnostics for d02pe, d02pf
• nag_ode_ivp_rkts_errass
• d02qf – Ordinary differential equations, initial value problem, Adams' method with root-finding (direct communication, comprehensive)
• nag_ode_ivp_adams_roots
• d02qg – Ordinary differential equations, initial value problem, Adams' method with root-finding (reverse communication, comprehensive)
• nag_ode_ivp_adams_roots_revcom
• d02qw – Ordinary differential equations, initial value problem, setup for d02qf and d02qg
• nag_ode_ivp_adams_setup
• d02qx – Ordinary differential equations, initial value problem, diagnostics for d02qf and d02qg
• nag_ode_ivp_adams_diag
• d02qy – Ordinary differential equations, initial value problem, root-finding diagnostics for d02qf and d02qg
• nag_ode_ivp_adams_rootdiag
• d02qz – Ordinary differential equations, initial value problem, interpolation for d02qf or d02qg
• nag_ode_ivp_adams_interp
• d02ra – Ordinary differential equations, general nonlinear boundary value problem, finite difference technique with deferred correction, continuation facility
• nag_ode_bvp_fd_nonlin_gen
• 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
• d02tg – nth-order linear ordinary differential equations, boundary value problem, collocation and least squares
• nag_ode_bvp_coll_nth_comp
• d02tl – Ordinary differential equations, general nonlinear boundary value problem, collocation technique (thread safe)
• nag_ode_bvp_coll_nlin_solve
• d02tv – Ordinary differential equations, general nonlinear boundary value problem, setup for d02tl
• nag_ode_bvp_coll_nlin_setup
• d02tx – Ordinary differential equations, general nonlinear boundary value problem, continuation facility for d02tl
• nag_ode_bvp_coll_nlin_contin
• d02ty – Ordinary differential equations, general nonlinear boundary value problem, interpolation for d02tl
• nag_ode_bvp_coll_nlin_interp
• d02tz – Ordinary differential equations, general nonlinear boundary value problem, diagnostics for d02tl
• nag_ode_bvp_coll_nlin_diag
• d02ua – Coefficients of Chebyshev interpolating polynomial from function values on Chebyshev grid
• nag_ode_bvp_ps_lin_coeffs
• d02ub – Function or low-order-derivative values on Chebyshev grid from coefficients of Chebyshev interpolating polynomial
• nag_ode_bvp_ps_lin_cgl_vals
• d02uc – Chebyshev Gauss–Lobatto grid generation
• nag_ode_bvp_ps_lin_cgl_grid
• d02ud – Differentiate a function by the FFT using function values on Chebyshev grid
• nag_ode_bvp_ps_lin_cgl_deriv
• d02ue – Solve linear constant coefficient boundary value problem on Chebyshev grid, Integral formulation
• nag_ode_bvp_ps_lin_solve
• d02uw – Interpolate a function from Chebyshev grid to uniform grid using barycentric Lagrange interpolation
• nag_ode_bvp_ps_lin_grid_vals
• d02uy – Clenshaw–Curtis quadrature weights for integration using computed Chebyshev coefficients
• nag_ode_bvp_ps_lin_quad_weights
• d02uz – Chebyshev polynomial evaluation, T_k(x)
• nag_ode_bvp_ps_lin_cheb_eval
• 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
• d02xk – Ordinary differential equations, initial value problem, interpolation for D02M–N functions, C¹ interpolant
• nag_ode_ivp_stiff_c1_interp
• d02za – Ordinary differential equations, initial value problem, weighted norm of local error estimate for D02M–N functions
• nag_ode_ivp_stiff_errest
• Functions scheduled for withdrawal
  • d02pc – Ordinary differential equations, initial value problem, Runge–Kutta method, integration over range with output
  • nag_ode_ivp_rk_range
  • d02pd – Ordinary differential equations, initial value problem, Runge–Kutta method, integration over one step
  • nag_ode_ivp_rk_onestep
  • d02pv – Ordinary differential equations, initial value problem, setup for d02pc and d02pd
  • nag_ode_ivp_rk_setup
  • d02pw – Ordinary differential equations, initial value problem, resets end of range for d02pd
  • nag_ode_ivp_rk_reset_tend
  • d02px – Ordinary differential equations, initial value problem, interpolation for d02pd
  • nag_ode_ivp_rk_interp
  • d02py – Ordinary differential equations, initial value problem, integration diagnostics for d02pc and d02pd
  • nag_ode_ivp_rk_diag
  • d02pz – Ordinary differential equations, initial value problem, error assessment diagnostics for d02pc and d02pd
  • nag_ode_ivp_rk_errass
  • d02tk – Ordinary differential equations, general nonlinear boundary value problem, collocation technique
  • nag_ode_bvp_coll_nlin

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D03