ode

Object interface for ODE problems.

📝Syntax

problem = ode(name, value)
result = solve(problem, tfinal)
result = solve(problem, t0, tfinal)
[f, data] = solutionFcn(problem, tfinal)

📄Description

ode stores a differential equation problem and the settings used by solve and solutionFcn.

Call	Purpose
solve(problem, tfinal)	Integrates from InitialTime to tfinal.
solve(problem, t0, tfinal)	Integrates from t0; this call-specific start time overrides InitialTime.
solutionFcn(problem, tfinal)	Returns an interpolation function and the corresponding result object.

Main object properties:

Property	Accepted values	Effect
EquationType	'standard', 'fullyimplicit'	'standard' uses ODEFcn(t,y). 'fullyimplicit' uses residuals ODEFcn(t,y,yp).
Solver	'auto', 'autoswitch', 'nonstiff', 'stiff', solver names	Selects the integration method. 'auto' chooses from the problem type. 'autoswitch' can restart with a stiff method when stiffness is detected.
SolverOptions	Options object matching the selected solver	Stores tolerances, output function, step-size bounds, and solver-specific settings.
Parameters	Numeric vector or cell array	Passed after the standard arguments to the ODE, event, output, and event-response callbacks. A cell array expands to one argument per cell.
SeparateComplexParts	'off', 'on'	With 'on', complex states are integrated through separated real and imaginary parts, while returned results use the original complex shape.

Solver families:

Family	Solver values	Notes
Nonstiff	'ode23', 'ode45', 'ode78', 'ode89', 'ode113'	Use for smooth explicit problems.
Stiff or mass matrix	'ode15s', 'ode23s', 'ode23t', 'ode23tb'	Use when a problem has fast decaying modes, a mass matrix, or a useful Jacobian.
Fully implicit	'ode15i', 'idas'	'idas' is available only when Nelson is built with the optional SUNDIALS backend.
Optional backend	'cvodesnonstiff', 'cvodesstiff', 'idas'	NELSON_SUNDIALS_RUNTIME can be OFF to force the in-tree fallback or ON to allow the backend when compiled.

💡Examples

Use InitialTime with a final time.

problem = ode('ODEFcn', @(t,y) -y, 'InitialTime', 2, 'InitialValue', 1);
result = solve(problem, 3)

Build an interpolation function.

problem = ode('ODEFcn', @(t,y) -y, 'InitialValue', 1);
f = solutionFcn(problem, 1);
yhalf = f(0.5)

Solve a fully implicit residual problem.

problem = ode('EquationType', 'fullyimplicit', ...
  'ODEFcn', @(t,y,yp) yp + y, ...
  'InitialValue', 1, ...
  'InitialSlope', -1);
result = solve(problem, 1)

Pass extra parameters to a problem function.

problem = ode('ODEFcn', @(t,y,a) a .* y, ...
  'InitialValue', 1, ...
  'Parameters', 2);
result = solve(problem, 0, 1)

Solve a problem by separating complex parts internally.

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

🕔Version History

Version	Description
2.0.0	initial version

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