Single-Step Variable-Order Runge-Kutta ODE Matlab script

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Single-Step Variable-Order Runge-Kutta ODE Solution - Variable oder (2,3,5) ODE solution that returns after each successful step. ODESS advances the numerical solution of a set of differential equations one step from t to t h. A variable order Runge-Kutta algorithm is used, where a 5th order step of length h is taken. If this step fails, the same derivative calculations are used to take a 3rd order step of length 3*h/5.If this step fails, the same derivative calculations are used to take a 2nd order step of length h/5. If all these attempts fail, a revised step length h is computed and the process repeats until a step succeeds. This mechanism is well suited for differential equations that have discontinuities or sharp changes appearing at unknown times. ODESS advances the solution a single time step from t to t h, thereby providing intimate access to the solution and ODE parameters every step.[T,Y,YP]=ODESS(ODEFUN,t,y,yp) integrates the first order differential equations computed in the M-file ODEFUN(t,y) from the time point t where y = y(t) and yp = ODEFUN(t,y). ODEFUN must be a function handle and must return a column vector of derivatives given the time t and vector y. [T,Y,YP] are the results at the time T = t h, where Y=Y(T) is a row vector of the solution, and YP=ODEFUN(T,Y) is a row vector of the slopes. ODESS('PName1',PValue1,'PName2',PValue2,...) sets ODESS parameters to the corresponding property values.ODESS(P) sets parameters using the structure P having fieldnames equal to parameter names and corresponding contents equal to property values. ODESS('Reset') resets all parameters to their default values including 'NextStep' so that a new problem may be started. ODESS('PName') returns the value associated with the parameter 'PName'. ODESS({'PName1' 'PName2' ...}) returns parameter values associated with the listed property values in a cell array. P=ODESS with no input argument returns a structure P of all settable parameter values as described above.Parameter DefaultName Value Limits Description'RelTol' 1e-3 >1e-10 Relative Error Tolerance'AbsTol' 1e-6 >0 Absolute Error Tolerance'MinStep' 1e-10 >1e-12 Minimum Stepsize, Hmin'MaxStep' 1 >=Hmin Maximum Stepsize'NextStep' [] >=Hmin Next Stepsize, Hnext'SafetyFactor' 0.9 (0.75,.95) Stepsize Safety Factor'GrowthLimit' 5 (2,20) Stepsize Growth Limit Ratio'ShrinkLimit' 0.1 (.05,.5) Stepsize Shrink Limit Ratio'FallBack' 'on' ('on','off') Enable Fall Back on Full Step Failure Requirements: · MATLAB Release: R14SP1
Operating system:
Windows / Linux / Mac OS / BSD / Solaris

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