Finding all real solutions of nonlinear systems of equations with discontinuities by a modified affine arithmetic

Chemical engineering is a rich area when comes to nonlinear systems of equations, possibly with multiple solutions, (unbounded) discontinuities, or functions which become undefined in terms of real values. In this work, a new approach is proposed for finding all real solutions of such systems within prescribed bounds. A modified affine arithmetic is used in an interval Newton method plus generalized bisection. A special constraint propagation is used to automatically remove regions where the functions are undefined for real numbers. Results for test problems have shown that the proposed implementation requires less computation effort than similar methods available in the literature for small continuous systems. Further, the method is able to find all real solutions of nonlinear systems of equations even when there are unbounded discontinuities or when functions become undefined within the given variable bounds.

► A modified interval-Newton method is described.
► A modified affine arithmetic (AA) is used instead of ordinary interval arithmetic.
► AA provides tighter and more descriptive bounds, reducing the computational cost.
► The method can handle discontinuities.
► The method can handle functions that become undefined in terms of real numbers.