`odeJacobian`

Supplies the Jacobian of an ODE to an ode object.

Category: Other public functions: funfun

Syntax

J = odeJacobian(Jacobian=fcn)

Creates a Jacobian definition from a function @(t, y) returning the matrix of derivatives.

J = odeJacobian(Jacobian=fcn, SparsityPattern=S)

Also declares which entries can be nonzero.

Description

Implicit solvers such as ode15s solve a nonlinear system at every step and need the Jacobian of the right-hand side. If it is not given, it is estimated by finite differences, which costs extra evaluations. Giving the exact Jacobian makes stiff problems faster and more reliable. For large systems the sparsity pattern lets the solver skip entries that are always zero.

Input arguments

Jacobian: Function handle, or a constant matrix, with the derivative of the right-hand side with respect to the state.
SparsityPattern: Sparse logical matrix marking the entries that may be nonzero.

Output arguments

J: An odeJacobian object, assigned to the Jacobian property of an ode object.

Example

Exact Jacobian for a stiff solver

J = odeJacobian(Jacobian=@(t, y) -1);
f = ode(ODEFcn=@(t, y) -y, InitialValue=1, Jacobian=J, Solver='ode15s');
sol = solve(f, 0, 1);
fprintf('%.3f\n', sol.Solution(end))

Output

0.368

odeJacobian