Numerical Methods for Solving Initial Value Problems on the Infinity Computer

被引：0
|
作者：
Sergeyev, Ya. D. [1 ,2 ]
Mukhametzhanov, M. S. [1 ,2 ]
Mazzia, F. [3 ]
Iavernaro, F. [3 ]
Amodio, P. [3 ]
机构：
[1] Univ Calabria, DIMES, I-87030 Commenda Di Rende, Italy
[2] Lobachevsky State Univ Nizhni Novgorod, Dept Software & Supercomp Technol, Nizhnii Novgorod, Russia
[3] Univ Bari, Dipartimento Matemat, I-70121 Bari, Italy
来源：
INTERNATIONAL JOURNAL OF UNCONVENTIONAL COMPUTING | 2016年 / 12卷 / 01期
基金：
俄罗斯科学基金会;
关键词：
Ordinary differential equations; initial value problem; numerical infinitesimals; Infinity Computer; ORDINARY DIFFERENTIAL-EQUATIONS; BLINKING FRACTALS; TURING-MACHINES; INFINITESIMALS; COMPUTATIONS;
D O I：
暂无
中图分类号：
TP301 [理论、方法];
学科分类号：
081202 ;
摘要：
New algorithms for the numerical solution of Ordinary Differential Equations (ODEs) with initial condition are proposed. They are designed for work on a new kind of a supercomputer - the Infinity Computer, - that is able to deal numerically with finite, infinite and infinitesimal numbers. Due to this fact, the Infinity Computer allows one to calculate the exact derivatives of functions using infinitesimal values of the stepsize. As a consequence, the new methods described in this paper are able to work with the exact values of the derivatives, instead of their approximations.
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页码：3 / 23
页数：21
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