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DotNumerics Functions list:
dn_AdamsMoulton(3)  (ode,y(x),xmax) uses the AdamsMoulton method. dn_AdamsMoulton(4)  (ode,y(x),xmax,steps) uses the AdamsMoulton method. dn_AdamsMoulton(5)  (ics,xmin,xmax,steps,D(x,y)) uses the AdamsMoulton method. dn_ExplicitRK45(3)  (ode,y(x),xmax) uses the explicit RungeKutta (4)5 method. dn_ExplicitRK45(4)  (ode,y(x),xmax,steps) uses the explicit RungeKutta (4)5 method. dn_ExplicitRK45(5)  (ics,xmin,xmax,steps,D(x,y)) uses the explicit RungeKutta (4)5 method. dn_GearsBDF(3)  (ode,y(x),xmax) uses the Gear’s BDF method. dn_GearsBDF(4)  (ode,y(x),xmax,steps) uses the Gear’s BDF method. dn_GearsBDF(5)  (ics,xmin,xmax,steps,D(x,y)) uses the Gear’s BDF method. dn_ImplicitRK5(3)  (ode,y(x),xmax) uses the implicit RungeKutta 5 method. dn_ImplicitRK5(4)  (ode,y(x),xmax,steps) uses the implicit RungeKutta 5 method. dn_ImplicitRK5(5)  (ics,xmin,xmax,steps,D(x,y)) uses the implicit RungeKutta 5 method. dn_LinAlgEigenvalues(1)  ( A ) computes the eigenvalues of a square matrix (general, symmetric, symmetric band and complex general matrices). dn_LinAlgEigenvectors(1)  ( A ) computes the eigenvectors of a square matrix (general, symmetric, symmetric band and complex general matrices). dn_LinAlgLLS_COF(2)  ( A, B ) computes the minimumnorm solution to a real linear least squares problem. Using a omplete orthogonal factorization of A. dn_LinAlgLLS_QRorLQ(2)  ( A, B ) computes the minimumnorm solution to a real linear least squares problem. Using a QR or LQ factorization of A. dn_LinAlgLLS_SVD(2)  ( A, B ) computes the minimumnorm solution to a real linear least squares problem. Using the singular value decomposition of A. dn_LinAlgSolve(2)  ( A, B ) computes the solution to a real system of linear equations (general, band and tridiagonal matrices): A * X = B. dn_LinAlgSVD(1)  ( A ) computes the singular value decomposition (SVD) of a real MbyN matrix: A = U * S * transpose(V). dn_MatrixInverse(1)  ( A ) calculate the inverse matrix.
Differential Equations. Initialvalue problem for nonstiff and stiff ordinary differential equations ODEs (explicit RungeKutta, implicit RungeKutta, Gear’s BDF and AdamsMoulton). Solvers for NonStiff Systems: dn_AdamsMoulton(init, x1, x2, intvls, D) solves an initialvalue problem for nonstiff ordinary differential equations using the AdamsMoulton method. dn_ExplicitRK45(init, x1, x2, intvls, D) solves an initialvalue problem for nonstiff ordinary differential equations using the explicit RungeKutta method of order (4)5. Solvers for Stiff Systems: dn_ImplicitRK5(init, x1, x2, intvls, D) solves an initialvalue problem for stiff ordinary differential equations using the implicit RungeKutta method of order 5. dn_GearsBDF(init, x1, x2, intvls, D) solves an initialvalue problem for stiff ordinary differential equations using the Gear’s BDF 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 10⁻⁷.  RelTol  relative tolerance parameter, default value 10⁻⁴. Links: 1. DotNumerics is a website dedicated to numerical computing for .NET. DotNumerics includes a Numerical Library for .NET. The library is written in pure C# and has more than 100,000 lines of code with the most advanced algorithms for Linear Algebra, Differential Equations and Optimization problems. The Linear Algebra library includes CSLapack, CSBlas and CSEispack, these libraries are the translation from Fortran to C# of LAPACK, BLAS and EISPACK, respectively. 2. Arenstorf orbit. Numerical Analysis: Theory and Applications. Proseminar, 28.03.2011, UIBK [pdf]. 3. How to find spatial periodic orbits around the Moon in the TBP. Books: 1. Solving Ordinary Differential Equations II: Stiff and DifferentialAlgebraic Problems. Examples: dn.ode.kinetic1.sm (9kb) downloaded 76 time(s). dn.ode.kinetic2.sm (13kb) downloaded 59 time(s). dn.ode.kinetic3.sm (13kb) downloaded 57 time(s). dn.ode.test1.sm (20kb) downloaded 64 time(s). dn.ode.test2.sm (19kb) downloaded 64 time(s). dn.ode.Amplitude detector.sm (21kb) downloaded 66 time(s). dn.ode.kinetic1.pdf (78kb) downloaded 64 time(s). dn.ode.kinetic2.pdf (94kb) downloaded 45 time(s). dn.ode.kinetic3.pdf (92kb) downloaded 41 time(s). dn.ode.test1.pdf (116kb) downloaded 41 time(s). dn.ode.test2.pdf (121kb) downloaded 42 time(s). dn.ode.Amplitude detector.pdf (149kb) downloaded 44 time(s).See also:● Mathcad Toolbox● SADEL● Matlab C++ Math Library● OSLO● lsoda● GNU Scientific Library (GSL)Edited by user 12 December 2021 23:24:11(UTC)
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Russia ☭ forever Viacheslav N. Mezentsev 
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