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On numerical simulation of partial differential equations in infinite precision. (English) Zbl 0947.65124

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.

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

Software:

Algorithm 693
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