MATLAB: ODE 45 Error unable to meet integration tolerance

cash karp methodnonsmooth solutionode45

Hello All, I am experiencing an error with ODE 45 unable to meet integration tolerance without reducing the time step below a minimum value. I read through the help files it is because of non smooth functions which are not handled in ODE45 Dormand–Prince (RKDP) method. There is another RK method Embedded Runga Kutta method by Cash-karper which deals with nonsmooth functions. Embedded Runga Kutta method by cash karper is also a variable step size Runga kutta method. Does Cash karper method overcomes the disadvantage of Runga kutta method i.e not able to handle non smooth function?. Does matlab have Cash Karper implementation of Runga Kutta ? . Any suggestions are highly appreciated.

Best Answer

The Symbolic Toolbox has some support for Cash-Karp methods: See http://www.mathworks.com/help/symbolic/mupad_ref/numeric-odesolve.html and https://www.mathworks.com/help/symbolic/mupad_ref/numeric-butcher.html

Related Solutions

MATLAB: Can I use numeric::odesolve as a replacement to ode45

It is possible, by using some magic. See for example,

syms y(t)
%Boundary conditions are required
eqns = {diff(y(t),t) == t*sin(y(t)), y(0) == 2};   %use a cell array! 
numdig = 16;     %number of decimal places to use
digits(numdig);
symLIST = @(varargin)feval(symengine,'DOM_LIST',varargin{:});
symRANGE = @(a,b) feval(symengine, '_range', a, b);
IVP = symLIST(eqns{:});
fields = symLIST(y(t));
IVP = feval(symengine,'numeric::ode2vectorfield', IVP, fields);
syms CK45
method = CK45;
feval(symengine, 'numeric::odesolve', IVP(1), symRANGE(IVP(2),10), IVP(3), method)

You can omit the method parameter from the call.

MATLAB: Can I use the ode45 solver for the state update in a unscented Kalman filter

You cannot use the ode45 function directly in the above example code as it will output integrated function values for all the time points instead of a single time-step value as required here. However, you can implement single-step updates of higher order methods such as Runge-Kutta ( https://en.wikipedia.org/wiki/Runge%2525E2%252580%252593Kutta_methods ) instead of the Euler method for better accuracy.

ode45 function itself uses an explicit Runge-Kutta formula, the Dormand-Prince pair (refer to the documentation page https://www.mathworks.com/help/matlab/ref/ode45.html#bu0200e-1)

You can find more information on other ODE integration methods related to this here https://blogs.mathworks.com/cleve/2014/05/26/ordinary-differential-equation-solvers-ode23-and-ode45/

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Related Solutions

MATLAB: Can I use numeric::odesolve as a replacement to ode45

MATLAB: Can I use the ode45 solver for the state update in a unscented Kalman filter

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