TY - GEN
T1 - Round-off error analysis of explicit one-step numerical integration methods
AU - Boldo, Sylvie
AU - Faissole, Florian
AU - Chapoutot, Alexandre
N1 - Publisher Copyright:
© 2017 IEEE.
PY - 2017/8/30
Y1 - 2017/8/30
N2 - Ordinary differential equations are ubiquitous in scientific computing. Solving exactly these equations is usually not possible, except for special cases, hence the use of numerical schemes to get a discretized solution. We are interested in such numerical integration methods, for instance Euler's method or the Runge-Kutta methods. As they are implemented using floating-point arithmetic, round-off errors occur. In order to guarantee their accuracy, we aim at providing bounds on the round-off errors of explicit one-step numerical integration methods. Our methodology is to apply a fine-grained analysis to these numerical algorithms. Our originality is that our floating-point analysis takes advantage of the linear stability of the scheme, a mathematical property that vouches the scheme is well-behaved.
AB - Ordinary differential equations are ubiquitous in scientific computing. Solving exactly these equations is usually not possible, except for special cases, hence the use of numerical schemes to get a discretized solution. We are interested in such numerical integration methods, for instance Euler's method or the Runge-Kutta methods. As they are implemented using floating-point arithmetic, round-off errors occur. In order to guarantee their accuracy, we aim at providing bounds on the round-off errors of explicit one-step numerical integration methods. Our methodology is to apply a fine-grained analysis to these numerical algorithms. Our originality is that our floating-point analysis takes advantage of the linear stability of the scheme, a mathematical property that vouches the scheme is well-behaved.
UR - https://www.scopus.com/pages/publications/85031669830
U2 - 10.1109/ARITH.2017.22
DO - 10.1109/ARITH.2017.22
M3 - Conference contribution
AN - SCOPUS:85031669830
T3 - Proceedings - 24th IEEE Symposium on Computer Arithmetic, ARITH 2017
SP - 82
EP - 89
BT - Proceedings - 24th IEEE Symposium on Computer Arithmetic, ARITH 2017
A2 - de Dinechin, Florent
A2 - Burgess, Neil
A2 - Bruguera, Javier
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 24th IEEE Symposium on Computer Arithmetic, ARITH 2017
Y2 - 24 July 2017 through 26 July 2017
ER -