A Geometric Level Set Method for Transcendental Equations from Chemical Engineering
Chadia A ane, Saâd Biaz, Said S.E.H. Elnashaie, Frank Uhlig · 2009
When trying to solve a single transcendental equation f (x, a) = 0 that depends on two parameters x and a, we have found the standard root finders such as bisection and Newton’s method lacking within the parameter range of a with multiple roots. Here we propose, implement, and test a level set method for solving parameterized transcendental equations with bifurcation. We create the elevation matrix data Z = f (x, a) ∈ Rn,n for x and a data vectors in Rn and draw the level zero contour curve for the associated surface (x, a, f (x, a)) ∈ R3 via data interpolation. The method is very simply implemented via MATLAB’s built-in contour command. It works exceedingly well and is much faster than using standard root finders that generally fail do give useful information near the bifurcation points or using continuation methods.