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GNU Scientific Library (GSL) Functions list:
gslbsimp(1)  (cmd) implicit BulirschStoer method of Bader and Deuflhard. gslbsimp(3)  (ode,y(x),xmax) implicit BulirschStoer method of Bader and Deuflhard. gslbsimp(4)  (ode,y(x),xmax,steps) implicit BulirschStoer method of Bader and Deuflhard. gslbsimp(5)  (ics,xmin,xmax,steps,D(x,y)) implicit BulirschStoer method of Bader and Deuflhard. gslbsimp(6)  (ics,xmin,xmax,steps,D(x,y),J(x,y)) implicit BulirschStoer method of Bader and Deuflhard. gslmsadams(1)  (cmd) variablecoefficient linear multistep Adams method in Nordsieck form. gslmsadams(3)  (ode,y(x),xmax) variablecoefficient linear multistep Adams method in Nordsieck form. gslmsadams(4)  (ode,y(x),xmax,steps) variablecoefficient linear multistep Adams method in Nordsieck form. gslmsadams(5)  (ics,xmin,xmax,steps,D(x,y)) variablecoefficient linear multistep Adams method in Nordsieck form. gslmsdbf(1)  (cmd) variablecoefficient linear multistep backward differentiation formula (BDF) method in Nordsieck form. gslmsdbf(3)  (ode,y(x),xmax) variablecoefficient linear multistep backward differentiation formula (BDF) method in Nordsieck form. gslmsdbf(4)  (ode,y(x),xmax,steps) variablecoefficient linear multistep backward differentiation formula (BDF) method in Nordsieck form. gslmsdbf(5)  (ics,xmin,xmax,steps,D(x,y)) variablecoefficient linear multistep backward differentiation formula (BDF) method in Nordsieck form. gslmsdbf(6)  (ics,xmin,xmax,steps,D(x,y),J(x,y)) variablecoefficient linear multistep backward differentiation formula (BDF) method in Nordsieck form. gslrk1imp(1)  (cmd) implicit Gaussian first order RungeKutta (implicit Euler or backward Euler) method. gslrk1imp(3)  (ode,y(x),xmax) implicit Gaussian first order RungeKutta (implicit Euler or backward Euler) method. gslrk1imp(4)  (ode,y(x),xmax,steps) implicit Gaussian first order RungeKutta (implicit Euler or backward Euler) method. gslrk1imp(5)  (ics,xmin,xmax,steps,D(x,y)) implicit Gaussian first order RungeKutta (implicit Euler or backward Euler) method. gslrk1imp(6)  (ics,xmin,xmax,steps,D(x,y),J(x,y)) implicit Gaussian first order RungeKutta (implicit Euler or backward Euler) method. gslrk2(1)  (cmd) explicit embedded RungeKutta (2,3) method. gslrk2(3)  (ode,y(x),xmax) explicit embedded RungeKutta (2,3) method. gslrk2(4)  (ode,y(x),xmax,steps) explicit embedded RungeKutta (2,3) method. gslrk2(5)  (ics,xmin,xmax,steps,D(x,y)) explicit embedded RungeKutta (2,3) method. gslrk2imp(1)  (cmd) implicit Gaussian second order RungeKutta (implicit midpoint) method. gslrk2imp(3)  (ode,y(x),xmax) implicit Gaussian second order RungeKutta (implicit midpoint) method. gslrk2imp(4)  (ode,y(x),xmax,steps) implicit Gaussian second order RungeKutta (implicit midpoint) method. gslrk2imp(5)  (ics,xmin,xmax,steps,D(x,y)) implicit Gaussian second order RungeKutta (implicit midpoint) method. gslrk2imp(6)  (ics,xmin,xmax,steps,D(x,y),J(x,y)) implicit Gaussian second order RungeKutta (implicit midpoint) method. gslrk4(1)  (cmd) explicit 4th order (classical) RungeKutta. Error estimation is carried out by the step doubling method. gslrk4(3)  (ode,y(x),xmax) explicit 4th order (classical) RungeKutta. Error estimation is carried out by the step doubling method. gslrk4(4)  (ode,y(x),xmax,steps) explicit 4th order (classical) RungeKutta. Error estimation is carried out by the step doubling method. gslrk4(5)  (ics,xmin,xmax,steps,D(x,y)) explicit 4th order (classical) RungeKutta. Error estimation is carried out by the step doubling method. gslrk4imp(1)  (cmd) implicit Gaussian second order RungeKutta (implicit midpoint) method. gslrk4imp(3)  (ode,y(x),xmax) implicit Gaussian second order RungeKutta (implicit midpoint) method. gslrk4imp(4)  (ode,y(x),xmax,steps) implicit Gaussian second order RungeKutta (implicit midpoint) method. gslrk4imp(5)  (ics,xmin,xmax,steps,D(x,y)) implicit Gaussian second order RungeKutta (implicit midpoint) method. gslrk4imp(6)  (ics,xmin,xmax,steps,D(x,y),J(x,y)) implicit Gaussian second order RungeKutta (implicit midpoint) method. gslrk8pd(1)  (cmd) explicit embedded RungeKutta PrinceDormand (8,9) method. gslrk8pd(3)  (ode,y(x),xmax) explicit embedded RungeKutta PrinceDormand (8,9) method. gslrk8pd(4)  (ode,y(x),xmax,steps) explicit embedded RungeKutta PrinceDormand (8,9) method. gslrk8pd(5)  (ics,xmin,xmax,steps,D(x,y)) explicit embedded RungeKutta PrinceDormand (8,9) method. gslrkck(1)  (cmd) explicit embedded RungeKutta CashKarp (4,5) method. gslrkck(3)  (ode,y(x),xmax) explicit embedded RungeKutta CashKarp (4,5) method. gslrkck(4)  (ode,y(x),xmax,steps) explicit embedded RungeKutta CashKarp (4,5) method. gslrkck(5)  (ics,xmin,xmax,steps,D(x,y)) explicit embedded RungeKutta CashKarp (4,5) method. gslrkf45(1)  (cmd) explicit embedded RungeKutta CashKarp (4,5) method. gslrkf45(3)  (ode,y(x),xmax) explicit embedded RungeKutta CashKarp (4,5) method. gslrkf45(4)  (ode,y(x),xmax,steps) explicit embedded RungeKutta CashKarp (4,5) method. gslrkf45(5)  (ics,xmin,xmax,steps,D(x,y)) explicit embedded RungeKutta CashKarp (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 stepsize 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 stepsize 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 stepsize 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,nnul,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 NonStiff Systems: gslrk2(init, x1, x2, intvls, D) Explicit embedded RungeKutta (2, 3) method. gslrk4(init, x1, x2, intvls, D) Explicit 4th order (classical) RungeKutta. Error estimation is carried out by the step doubling method. gslrkf45(init, x1, x2, intvls, D) Explicit embedded RungeKuttaFehlberg (4, 5) method. gslrkck(init, x1, x2, intvls, D) Explicit embedded RungeKutta CashKarp (4, 5) method. gslrk8pd(init, x1, x2, intvls, D) Explicit embedded RungeKutta PrinceDormand (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 righthand side of the system Options:  AbsTol  absolute tolerance parameter, default value 1E7.  RelTol  relative tolerance parameter, default value 1E4. Examples: gsl.ode.integrate.sm (12kb) downloaded 64 time(s). gsl.ode.kinetic1.sm (9kb) downloaded 62 time(s). gsl.ode.kinetic2.sm (15kb) downloaded 57 time(s). gsl.ode.kinetic3.sm (15kb) downloaded 54 time(s). gsl.ode.test1.sm (20kb) downloaded 57 time(s). gsl.ode.test2.sm (19kb) downloaded 55 time(s). gsl.ode.Amplitude detector.sm (21kb) downloaded 73 time(s). gsl.ode.integrate.pdf (93kb) downloaded 59 time(s). gsl.ode.kinetic1.pdf (78kb) downloaded 54 time(s). gsl.ode.kinetic2.pdf (93kb) downloaded 46 time(s). gsl.ode.kinetic3.pdf (92kb) downloaded 40 time(s). gsl.ode.test1.pdf (111kb) downloaded 44 time(s). gsl.ode.test2.pdf (111kb) downloaded 46 time(s). gsl.ode.Amplitude detector.pdf (149kb) downloaded 53 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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