ODE87 is a realization of explicit Runge-Kutta method. Integrates a system of ordinary differential equations using 8-7 th order Dorman and Prince formulas. See P.J. Prince & J.R. Dorman (1981) High order embedded Runge-Kutta formulae. J.Comp. Appl. Math., Vol. 7. p.67-75.
This is a 8th-order accurate integrator therefore the local error normally expected is O(h^9). This requires 13 function evaluations per integration step.
Some information about method can be found in Hairer, Norsett and Wanner (1993): Solving Ordinary Differential Equations. Nonstiff Problems. 2nd edition. Springer Series in Comput. Math., vol. 8.
Interface to program based on standart MATLAB ode-suite interface but with some restriction.
This file is intended for use with MATLAB and was produced for MATDS-program (see http://www.math.rsu.ru/mexmat/kvm/matds/)
Vasiliy Govorukhin (2020). ode87 Integrator (https://www.mathworks.com/matlabcentral/fileexchange/3616-ode87-integrator), MATLAB Central File Exchange. Retrieved .
Can this file integrate in case of specific time steps? I mean if [tspan] has more than two elements can it integrate?
Perfect working!!! Thank you very much
Fast. About 4 times speed up compared to a custom rk4 scheme I was using to solve Hamiltonian equations.
can anybody help me to understand how to use it in MATLAB? How to use it with my ode? If I run this file it shows the error at line 79. Please help me ASAP.
I need to integrate orbit-problems
I used this for integrating Schroedinger equation in Quantum Mechanics for a three-level system. As opposed to ode45, ode87 preserves normalization to a good extent (one part in 10^4 in my case).
ok, is good integration
iam worke in university of basrah
Very good commented, clear easyly understandable, good for learning, the only thing involved in such a method would be truncation error ? (large number of floating point operations) but thanks to this code I was able to understand Runge Kutta Excellent job!
Fast, works with R13, R14 also.