ERCSJ

Extrapolated Rosebrock method with complex step Jacobian estimator for numerical Integration of stiff ordinary differential equation that admit a holomorphic extension.

Syntax

[t_sol, x_sol] = ercsj(f, tspan, x0);

Solves the differential equation $x' = f(t,x)$. f is a function handle with 2 arguments: $t$ as the time and $x$ as the state variable, in that order. $f$ must return a column vector or a scalar. tspan$=[t_0, T_f]$ defines the integration interval. The initial condition is given by $x(t_0) =$ x0. The numerical solution of the state variable at the times given by t_sol is x_sol.

[t_sol, x_sol] = ercsj(f, tspan, x0, Rtol);
[t_sol, x_sol] = ercsj(f, tspan, x0, Rtol, Atol);

Rtol is the relative error tolerance (1e-3 by default) of the numerical method. Atol is the absolute error tolerance (1e-6 by default).

Tests

test_ERCSJ(case_num=1, fixed_h=false, get_hdata=true, do_comparison=false);

Runs the method on a test case determined by case_num and plots the ouput. There are 15 test cases, so case_num must be an integer between 1 and 15. The flag fixed_h specifies whether to use a fixed step size (predefined for each test case), or an adaptive step size. If an adaptive step size is used, the flag get_hdata specifies whether or not to plot the step sizes (in log scale, with rejected step sizes marked) and the cubic root of the estimated discretization errors. If do_comparison is true then the test case will also be solved with MATLAB's ode23tb solver, including the results in the plots for comparison.