Imai, Hitoshi; Takeuchi, Toshiki; Kushida, Masahiro On numerical simulation of partial differential equations in infinite precision. (English) Zbl 0947.65124 Adv. Math. Sci. Appl. 9, No. 2, 1007-1016 (1999). A numerical simulation in arbitrary precision for partial differential equations is presented. For smooth solutions the high accuracy of spectral methods is demonstrated. Spectral methods are used for the control of truncation errors and multiple precision arithmetic for the control of rounding errors. For some model problems high precision is observed in numerical results. Reviewer: W.Heinrichs (Essen) MSC: 65N35 Spectral, collocation and related methods for boundary value problems involving PDEs 65G50 Roundoff error 35J25 Boundary value problems for second-order elliptic equations Keywords:numerical simulation; spectral methods; rounding errors; numerical results Software:Algorithm 693 PDFBibTeX XMLCite \textit{H. Imai} et al., Adv. Math. Sci. Appl. 9, No. 2, 1007--1016 (1999; Zbl 0947.65124)