An interface representing a univariate real function.

When a user-defined function encounters an error during evaluation, the value method should throw a user-defined unchecked exception.

The following code excerpt shows the recommended way to do that using a root solver as an example, but the same construct is applicable to ODE integrators or optimizers.

private static class LocalException extends RuntimeException {
    // The x value that caused the problem.
    private final SomeFieldType x;

    public LocalException(SomeFieldType x) {
        this.x = x;
    }

    public double getX() {
        return x;
    }
}

private static class MyFunction implements FieldUnivariateFunction<SomeFieldType> {
    public SomeFieldType value(SomeFieldType x) {
        SomeFieldType y = hugeFormula(x);
        if (somethingBadHappens) {
          throw new LocalException(x);
        }
        return y;
    }
}

public void compute() {
    try {
        solver.solve(maxEval, new MyFunction(a, b, c), min, max);
    } catch (LocalException le) {
        // Retrieve the x value.
    }
}

As shown, the exception is local to the user's code and it is guaranteed that Apache Commons Math will not catch it.