ode complex workflow tutorial

Solve object ODE problems with complex states.

📄Description

Use SeparateComplexParts with the object workflow when an equation is written with complex states but the integration should advance separated real and imaginary parts internally.

Mode	Setting	Behavior
Native complex	SeparateComplexParts = 'off'	Use complex values directly when the selected solver supports them.
Separated real system	SeparateComplexParts = 'on'	Integrate real and imaginary parts as a real system.
Returned shape	Original initial state shape.	Results are reshaped back to the user's state layout.

User functions receive complex values. The returned result object also stores complex Solution and EventSolution arrays.

The same workflow supports interpolation with deval, event objects, output functions, mass matrices, Jacobians, and fully implicit equations.

💡Examples

Solve a scalar complex problem.

problem = ode('ODEFcn', @(t,y) y .* t + 2 * 1i, ...
  'InitialValue', 1 + 1i, ...
  'SeparateComplexParts', 'on');
result = solve(problem, 0, 2);
value = result.Solution(:, length(result.Time))

Interpolate a complex result.

problem = ode('ODEFcn', @(t,y) 1i * y, ...
  'InitialValue', 1, ...
  'SeparateComplexParts', 'on');
result = solve(problem, 0, 1);
yhalf = deval(result, 0.5)

Stop on a complex-state event.

event = odeEvent('EventFcn', @(t,y) imag(y) - 0.5, ...
  'Response', 'stop');
problem = ode('ODEFcn', @(t,y) 1 + 1i, ...
  'InitialValue', 0, ...
  'SeparateComplexParts', 'on', ...
  'EventDefinition', event);
result = solve(problem, 0, 1);
result.EventSolution

🔗See Also

ode odeEvent deval

🕔Version History

Version	Description
2.0.0	initial version

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