Effectiveness of Floating-Point Precision on the Numerical Approximation by Spectral Methods

• DOI: 10.3390/mca26020042
• Publication Date: 2021-05-27T01:56:44Z
• Authors: José A. O. Matos; Paulo B. Vasconcelos
• Keywords: Double-precision floating-point format; Toolbox; Machine epsilon; Spectral method; Order of accuracy

With the fast advances in computational sciences, there is a need for more accurate computations, especially large-scale solutions of differential problems and long-term simulations. Amid many numerical approaches to solving problems, including both local global methods, spectral methods can offer greater accuracy. The downside that often require high-order polynomial approximations, which brings instability issues problem resolution. In particular, large condition numbers associated with operational matrices, prevent stable algorithms from working within machine precision. Software-based implement arbitrary precision arithmetic are available should be explored obtain higher accuracy when needed, even computing time cost associated. this work, experimental results on computation approximate via detailed recourse quadruple arithmetic. Variable was used Tau Toolbox, mathematical software package solve integro-differential method.