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DotNumerics  Functions list:
dn_AdamsMoulton(3) - (ode,y(x),xmax) uses the Adams-Moulton method. dn_AdamsMoulton(4) - (ode,y(x),xmax,steps) uses the Adams-Moulton method. dn_AdamsMoulton(5) - (ics,xmin,xmax,steps,D(x,y)) uses the Adams-Moulton method. dn_ExplicitRK45(3) - (ode,y(x),xmax) uses the explicit Runge-Kutta (4)5 method. dn_ExplicitRK45(4) - (ode,y(x),xmax,steps) uses the explicit Runge-Kutta (4)5 method. dn_ExplicitRK45(5) - (ics,xmin,xmax,steps,D(x,y)) uses the explicit Runge-Kutta (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 Runge-Kutta 5 method. dn_ImplicitRK5(4) - (ode,y(x),xmax,steps) uses the implicit Runge-Kutta 5 method. dn_ImplicitRK5(5) - (ics,xmin,xmax,steps,D(x,y)) uses the implicit Runge-Kutta 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 minimum-norm solution to a real linear least squares problem. Using a omplete orthogonal factorization of A. dn_LinAlgLLS_QRorLQ(2) - ( A, B ) computes the minimum-norm solution to a real linear least squares problem. Using a QR or LQ factorization of A. dn_LinAlgLLS_SVD(2) - ( A, B ) computes the minimum-norm 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 M-by-N matrix: A = U * S * transpose(V). dn_MatrixInverse(1) - ( A ) calculate the inverse matrix.
Differential Equations. Initial-value problem for nonstiff and stiff ordinary differential equations ODEs (explicit Runge-Kutta, implicit Runge-Kutta, Gear’s BDF and Adams-Moulton). Solvers for Non-Stiff Systems: dn_AdamsMoulton(init, x1, x2, intvls, D) solves an initial-value problem for nonstiff ordinary differential equations using the Adams-Moulton method. dn_ExplicitRK45(init, x1, x2, intvls, D) solves an initial-value problem for nonstiff ordinary differential equations using the explicit Runge-Kutta method of order (4)5. Solvers for Stiff Systems: dn_ImplicitRK5(init, x1, x2, intvls, D) solves an initial-value problem for stiff ordinary differential equations using the implicit Runge-Kutta method of order 5. dn_GearsBDF(init, x1, x2, intvls, D) solves an initial-value 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 right-hand 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 Differential-Algebraic Problems. Examples:  dn.ode.kinetic1.sm (9kb) downloaded 88 time(s). dn.ode.kinetic2.sm (13kb) downloaded 65 time(s). dn.ode.kinetic3.sm (13kb) downloaded 64 time(s). dn.ode.test1.sm (20kb) downloaded 70 time(s). dn.ode.test2.sm (19kb) downloaded 69 time(s). dn.ode.Amplitude detector.sm (21kb) downloaded 73 time(s). dn.ode.kinetic1.pdf (78kb) downloaded 75 time(s). dn.ode.kinetic2.pdf (94kb) downloaded 53 time(s). dn.ode.kinetic3.pdf (92kb) downloaded 50 time(s). dn.ode.test1.pdf (116kb) downloaded 50 time(s). dn.ode.test2.pdf (121kb) downloaded 51 time(s). dn.ode.Amplitude detector.pdf (149kb) downloaded 52 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 (git.io/vOZo0) Viacheslav N. Mezentsev |
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on 13/07/2013(UTC), on 13/07/2013(UTC), on 13/07/2013(UTC), on 14/07/2013(UTC)
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