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Special
AiryAi, AiryBi, BesselI, BesselJ, BesselK, BesselY, Beta, Chi, Ci, Dawson, DiGamma, DiLog, Dirichlet_Eta, Dirichlet_Lambda, Ei, Erf, Erfc, FresnelCos, FresnelSin, Gamma, Gudermannian, HankelH1, HankelH2, Harmonic, Hypergeom_2F1, invGudermannian, KelvinBei, KelvinBer, KelvinKei, KelvinKer, LambertW, Li, LnGamma, PolyGamma, PolyLog, Psi, RK4, RK45, Shi, Si, Zeta

Algebra
Apart, Coefficient, Degree, Denominator, Divisors, DivisorSigma, Eval, Expand, Factor, GCD, LCM, PolyDivide, PolyFit, PolyGCD, PolyLCM, PowerExpand, Quotient, Remainder, Sequence, SimplifyPoly, Solve, SolveSystem, Together

Basic
Abs, Arg, Conj, Exp, Hyperbolic Functions, Im, Ln, Log, Re, Trigonometric Functions

Calculus
D, Diff, DSolve, fDiff, FourierCos, FourierSeries, FourierSin, iDiff, iLaplace, Integrate, Laplace, Limit, NIntegrate, pDiff, Product, Series, Sum

CAS
Append, Call, Caps, Char, Choose, Clear, Command, Date, Delete, Extract, Function, Insert, IsList, IsMatrix, IsNumber, IsPoly, Left, Length, List, Matrix, Part, Replace, Reshape, Reverse, Right, Size, Sort, String, Value, Variables

Data
Constant, Finance, HRStoHMS, LoadList, LoadMatrix, Table

Elementary
Binomial, Ceil, Eulerian, Factorial, Floor, fPart, iPart, Mod, Multinomial, nCr, nPr, nRoot, Pochhammer, Round, Sign, Sqrt

Graphing
clip, FullRectSineWave, HalfRectSineWave, SawToothWave, SquareWave, StaircaseWave, TriangleWave

Manual
Code Files, Commands, Creating Scripts, Entering Expressions, Graphing Equations, Include Folder, Lists, Matrices, Strings, Symbols, Time Graphing

Matrix
Cholesky, coFactor, Det, Eigenvalues, Eigenvectors, Identity, Inverse, LUDecomposition, QR, RowReduce, SVD, Transpose

Number
AlternatingSeries, Catalan, cFrac, Convergents, IsPrime, LegendreP, nFactors, nPrimes, Pi_Digits, Random

Plot
BodePlot, ContourPlot, CylindricalPlot3D, FractalPlot, ImagePlot, ImplicitPlot, JuliaPlot, ListPlot, ListPlot3D, MultiPlot, MultiPlot3D, ParametricPlot, ParametricPlot3D, Plot, Plot3D, PolarPlot, SphericalPlot3D, VectorPlot, VectorPlot3D

Scripting
Animate, CheckBox, Draw, DrawColor, DrawWindow, Else If, Error, If, Include, Loop, Message, Scroll, Trace, While

Special Polynomials
Bernoulli, ChebyshevT, ChebyshevU, Euler, Fibonacci, GegenbauerC, HermiteH, LaguerreL, LegendreQ, Lucas

Statistical
BinomialCDF, BinomialPDF, ChiSquareCDF, ChiSquarePDF, Fcdf, Fpdf, GeoCDF, GeoPDF, InverseNormal, Max, Mean, Min, NormalCDF, NormalPDF, PoissonCDF, PoissonPDF, StandardDeviation, StudentTCDF, StudentTPDF, Variance

Trigonometric
DEGtoDMS, ExpConvert, TrigCollect, TrigConvert, TrigExpand, TrigReduce

Vector Calculus
Angle, Cross, Curl, Divergence, Dot, Duf, Gradient, Hessian, Jacobian, Laplacian, Norm, SurfaceNormal
  
RK45(function, t, y, a, b, y0, Tol=10E-5, hmax=0.25, hmin=10E-6, N=20)
function
Expression or name of a script

t
Name of variable

y
Name of variable

a
Initial value of t

b
Final value of t

y0
Initial value

Tol=10E-5
Maximum tolerance

hmax=0.25
Maximum-sized step

hmin=10E-6
Minimum-sized step

N=20
Number of partitions in the domain [a,b]

The Runge–Kutta method.

Examples  

References
http://en.wikipedia.org/wiki/Runge%E2%80%93Kutta_methods
http://mathworld.wolfram.com/Runge-KuttaMethod.html

Related Functions
RK4



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