Domains for computation in mathematics, physics and exact real arithmetic

A new fractional sub-equation method for solving the space-time fractional differential equations in mathematical physics

In this paper, a new fractional sub-equation method is proposed for finding exact solutions of fractional partial differential equations (FPDEs) in the sense of modified Riemann-Liouville derivative. With the aid of symbolic computation, we choose the space-time fractional Zakharov-Kuznetsov-Benjamin-Bona-Mahony (ZKBBM) equation in mathematical physics with a source to illustrate the validity a...

The Principle of Relativity: From Ungar’s Gyrolanguage for Physics to Weaving Computation in Mathematics

‎This paper extends the scope of algebraic computation based on a non standard $times$ to ‎the more basic case of a non standard $+$‎, ‎where standard means associative ‎and commutative‎. ‎Two physically meaningful examples of a non standard $+$ are ‎provided by the observation of motion in Special Relativity‎, ‎from either ‎outside (3D) or inside (2D or more)‎, ‎We revisit the ``gyro''-theory ...

Coinductive Definitions and Real Numbers

Real number computation in modern computers is mostly done via floating point arithmetic which can sometimes produce wildly erroneous results. An alternative approach is to use exact real arithmetic whose results are guaranteed correct to any user-specified precision. It involves potentially infinite data structures and has therefore in recent years been studied using the mathematical field of ...

Exact soultion of full interval linear equation AX=B based on Kaucher arithmetic

European Projects

Traditional numerical methods for polynomial root computation are fast but they sometimes return wrong results. Algorithms from computer algebra, on the other hand, guarantee correctness but tend to require long computing times. The computing time can, however, be dramatically reduced if exact arithmetic is carefully replaced by floating point arithmetic and if, moreover, ways are found to empl...