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GNU Scientific Library (GSL)  Functions list:
gslbsimp(1) - (cmd) implicit Bulirsch-Stoer method of Bader and Deuflhard. gslbsimp(3) - (ode,y(x),xmax) implicit Bulirsch-Stoer method of Bader and Deuflhard. gslbsimp(4) - (ode,y(x),xmax,steps) implicit Bulirsch-Stoer method of Bader and Deuflhard. gslbsimp(5) - (ics,xmin,xmax,steps,D(x,y)) implicit Bulirsch-Stoer method of Bader and Deuflhard. gslbsimp(6) - (ics,xmin,xmax,steps,D(x,y),J(x,y)) implicit Bulirsch-Stoer method of Bader and Deuflhard. gslmsadams(1) - (cmd) variable-coefficient linear multistep Adams method in Nordsieck form. gslmsadams(3) - (ode,y(x),xmax) variable-coefficient linear multistep Adams method in Nordsieck form. gslmsadams(4) - (ode,y(x),xmax,steps) variable-coefficient linear multistep Adams method in Nordsieck form. gslmsadams(5) - (ics,xmin,xmax,steps,D(x,y)) variable-coefficient linear multistep Adams method in Nordsieck form. gslmsdbf(1) - (cmd) variable-coefficient linear multistep backward differentiation formula (BDF) method in Nordsieck form. gslmsdbf(3) - (ode,y(x),xmax) variable-coefficient linear multistep backward differentiation formula (BDF) method in Nordsieck form. gslmsdbf(4) - (ode,y(x),xmax,steps) variable-coefficient linear multistep backward differentiation formula (BDF) method in Nordsieck form. gslmsdbf(5) - (ics,xmin,xmax,steps,D(x,y)) variable-coefficient linear multistep backward differentiation formula (BDF) method in Nordsieck form. gslmsdbf(6) - (ics,xmin,xmax,steps,D(x,y),J(x,y)) variable-coefficient linear multistep backward differentiation formula (BDF) method in Nordsieck form. gslrk1imp(1) - (cmd) implicit Gaussian first order Runge-Kutta (implicit Euler or backward Euler) method. gslrk1imp(3) - (ode,y(x),xmax) implicit Gaussian first order Runge-Kutta (implicit Euler or backward Euler) method. gslrk1imp(4) - (ode,y(x),xmax,steps) implicit Gaussian first order Runge-Kutta (implicit Euler or backward Euler) method. gslrk1imp(5) - (ics,xmin,xmax,steps,D(x,y)) implicit Gaussian first order Runge-Kutta (implicit Euler or backward Euler) method. gslrk1imp(6) - (ics,xmin,xmax,steps,D(x,y),J(x,y)) implicit Gaussian first order Runge-Kutta (implicit Euler or backward Euler) method. gslrk2(1) - (cmd) explicit embedded Runge-Kutta (2,3) method. gslrk2(3) - (ode,y(x),xmax) explicit embedded Runge-Kutta (2,3) method. gslrk2(4) - (ode,y(x),xmax,steps) explicit embedded Runge-Kutta (2,3) method. gslrk2(5) - (ics,xmin,xmax,steps,D(x,y)) explicit embedded Runge-Kutta (2,3) method. gslrk2imp(1) - (cmd) implicit Gaussian second order Runge-Kutta (implicit mid-point) method. gslrk2imp(3) - (ode,y(x),xmax) implicit Gaussian second order Runge-Kutta (implicit mid-point) method. gslrk2imp(4) - (ode,y(x),xmax,steps) implicit Gaussian second order Runge-Kutta (implicit mid-point) method. gslrk2imp(5) - (ics,xmin,xmax,steps,D(x,y)) implicit Gaussian second order Runge-Kutta (implicit mid-point) method. gslrk2imp(6) - (ics,xmin,xmax,steps,D(x,y),J(x,y)) implicit Gaussian second order Runge-Kutta (implicit mid-point) method. gslrk4(1) - (cmd) explicit 4th order (classical) Runge-Kutta. Error estimation is carried out by the step doubling method. gslrk4(3) - (ode,y(x),xmax) explicit 4th order (classical) Runge-Kutta. Error estimation is carried out by the step doubling method. gslrk4(4) - (ode,y(x),xmax,steps) explicit 4th order (classical) Runge-Kutta. Error estimation is carried out by the step doubling method. gslrk4(5) - (ics,xmin,xmax,steps,D(x,y)) explicit 4th order (classical) Runge-Kutta. Error estimation is carried out by the step doubling method. gslrk4imp(1) - (cmd) implicit Gaussian second order Runge-Kutta (implicit mid-point) method. gslrk4imp(3) - (ode,y(x),xmax) implicit Gaussian second order Runge-Kutta (implicit mid-point) method. gslrk4imp(4) - (ode,y(x),xmax,steps) implicit Gaussian second order Runge-Kutta (implicit mid-point) method. gslrk4imp(5) - (ics,xmin,xmax,steps,D(x,y)) implicit Gaussian second order Runge-Kutta (implicit mid-point) method. gslrk4imp(6) - (ics,xmin,xmax,steps,D(x,y),J(x,y)) implicit Gaussian second order Runge-Kutta (implicit mid-point) method. gslrk8pd(1) - (cmd) explicit embedded Runge-Kutta Prince-Dormand (8,9) method. gslrk8pd(3) - (ode,y(x),xmax) explicit embedded Runge-Kutta Prince-Dormand (8,9) method. gslrk8pd(4) - (ode,y(x),xmax,steps) explicit embedded Runge-Kutta Prince-Dormand (8,9) method. gslrk8pd(5) - (ics,xmin,xmax,steps,D(x,y)) explicit embedded Runge-Kutta Prince-Dormand (8,9) method. gslrkck(1) - (cmd) explicit embedded Runge-Kutta Cash-Karp (4,5) method. gslrkck(3) - (ode,y(x),xmax) explicit embedded Runge-Kutta Cash-Karp (4,5) method. gslrkck(4) - (ode,y(x),xmax,steps) explicit embedded Runge-Kutta Cash-Karp (4,5) method. gslrkck(5) - (ics,xmin,xmax,steps,D(x,y)) explicit embedded Runge-Kutta Cash-Karp (4,5) method. gslrkf45(1) - (cmd) explicit embedded Runge-Kutta Cash-Karp (4,5) method. gslrkf45(3) - (ode,y(x),xmax) explicit embedded Runge-Kutta Cash-Karp (4,5) method. gslrkf45(4) - (ode,y(x),xmax,steps) explicit embedded Runge-Kutta Cash-Karp (4,5) method. gslrkf45(5) - (ics,xmin,xmax,steps,D(x,y)) explicit embedded Runge-Kutta Cash-Karp (4,5) method. gsl_deriv_backward(3) - (f,x,h) computes the numerical derivative of the function f at the point x using an adaptive backward difference algorithm with a step-size of h. gsl_deriv_central(3) - (f,x,h) computes the numerical derivative of the function f at the point x using an adaptive central difference algorithm with a step-size of h. gsl_deriv_forward(3) - (f,x,h) computes the numerical derivative of the function f at the point x using an adaptive forward difference algorithm with a step-size of h. gsl_sf_airy(1) - (cmd) compute the Airy function. gsl_sf_airy(2) - (flags,x) compute the Airy function. gsl_sf_bessel(1) - (cmd) compute the Bessel function. gsl_sf_bessel(2) - (flags,x) compute the Bessel function. gsl_sf_bessel(3) - (flags,n|nu|l,x) compute the Bessel function. gsl_sf_clausen(1) - (x) calculate the Clausen integral. gsl_sf_dawson(1) - (x) calculate the Dawson integral. gsl_sf_debye(2) - (n,x) calculate the Debye function. gsl_sf_dilog(1) - (x) calculate the Dilogarithm. gsl_sf_ellint_D(2) - (ϕ,k) compute the incomplete elliptic integral D(ϕ,k). gsl_sf_ellint_Dcomp(1) - (k) compute the complete elliptic integral D(k). gsl_sf_ellint_E(2) - (ϕ,k) compute the incomplete elliptic integral E(ϕ,k). gsl_sf_ellint_Ecomp(1) - (k) compute the complete elliptic integral E(k). gsl_sf_ellint_F(2) - (ϕ,k) compute the incomplete elliptic integral F(ϕ,k). gsl_sf_ellint_Kcomp(1) - (k) compute the complete elliptic integral K(k). gsl_sf_ellint_P(3) - (ϕ,k,n) compute the incomplete elliptic integral P(ϕ,k,n). gsl_sf_ellint_Pcomp(2) - (k,n) compute the complete elliptic integral Π(k,n). gsl_sf_ellint_RC(2) - (x,y) compute the incomplete elliptic integral RC(x,y). gsl_sf_ellint_RD(3) - (x,y,z) compute the incomplete elliptic integral RD(x,y,z). gsl_sf_ellint_RF(3) - (x,y,z) compute the incomplete elliptic integral RF(x,y,z). gsl_sf_ellint_RJ(4) - (x,y,z,p) compute the incomplete elliptic integral RJ(x,y,z,p). gsl_sf_eta(1) - (s) calculate the eta function η(s) for arbitrary s. gsl_sf_eta_int(1) - (n) calculate the eta function η(n) for integer n. gsl_sf_hzeta(2) - (s,q) calculate the Hurwitz zeta function ζ(s,q) for s > 1, q > 0. gsl_sf_zeta(1) - (s) calculate the Riemann zeta function ζ(s) for arbitrary s ≠ 1. gsl_sf_zetam1(1) - (s) calculate the Riemann zeta function ζ(s) minus one for arbitrary s ≠ 1. gsl_sf_zetam1_int(1) - (n) calculate the Riemann zeta function ζ(n) minus one for integer n ≠ 1. gsl_sf_zeta_int(1) - (n) calculate the Riemann zeta function ζ(n) for integer n ≠ 1. gsl_version - returns GSL version.
Solvers for Non-Stiff Systems: gslrk2(init, x1, x2, intvls, D) Explicit embedded Runge-Kutta (2, 3) method. gslrk4(init, x1, x2, intvls, D) Explicit 4th order (classical) Runge-Kutta. Error estimation is carried out by the step doubling method. gslrkf45(init, x1, x2, intvls, D) Explicit embedded Runge-Kutta-Fehlberg (4, 5) method. gslrkck(init, x1, x2, intvls, D) Explicit embedded Runge-Kutta Cash-Karp (4, 5) method. gslrk8pd(init, x1, x2, intvls, D) Explicit embedded Runge-Kutta Prince-Dormand (8, 9) method. Arguments: - init is either a vector of n real initial values, where n is the number of unknowns (or a single scalar initial value, in the case of a single ODE). - x1 and x2 are real, scalar endpoints of the interval over which the solution to the ODE(s) is evaluated. Initial values in init are the values of the ODE function(s) evaluated at x1. - intvls is the integer number of discretization intervals used to interpolate the solution function. The number of solution points is the number of intervals + 1. - D is a vector function of the form D(x,y) specifying the right-hand side of the system Options: - AbsTol - absolute tolerance parameter, default value 1E-7. - RelTol - relative tolerance parameter, default value 1E-4. Examples:   gsl.ode.integrate.sm (12kb) downloaded 101 time(s). gsl.ode.kinetic1.sm (9kb) downloaded 95 time(s). gsl.ode.kinetic2.sm (15kb) downloaded 83 time(s). gsl.ode.kinetic3.sm (15kb) downloaded 81 time(s). gsl.ode.test1.sm (20kb) downloaded 84 time(s). gsl.ode.test2.sm (19kb) downloaded 81 time(s). gsl.ode.Amplitude detector.sm (21kb) downloaded 111 time(s). gsl.ode.integrate.pdf (93kb) downloaded 86 time(s). gsl.ode.kinetic1.pdf (78kb) downloaded 77 time(s). gsl.ode.kinetic2.pdf (93kb) downloaded 65 time(s). gsl.ode.kinetic3.pdf (92kb) downloaded 60 time(s). gsl.ode.test1.pdf (111kb) downloaded 70 time(s). gsl.ode.test2.pdf (111kb) downloaded 69 time(s). gsl.ode.Amplitude detector.pdf (149kb) downloaded 83 time(s).Links:1. GNU Scientific Library – Reference Manual. 2. GSL for Windows. 3. The GSL Team. 4. Thanks. See also:● Mathcad Toolbox● DotNumerics● SADEL● Matlab C++ Math Library● OSLO● lsodaEdited by user 13 January 2022 10:35:18(UTC)
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