An ESDIRK Method with Sensitivity Analysis Capabilities

Morten Rode Kristensen, John Bagterp Jørgensen, Per Grove Thomsen, Sten Bay Jørgensen

Research output: Contribution to journalJournal articleResearchpeer-review

Abstract

A new algorithm for numerical sensitivity analysis of ordinary differential equations (ODEs) is presented. The underlying ODE solver belongs to the Runge-Kutta family. The algorithm calculates sensitivities with respect to problem parameters and initial conditions, exploiting the special structure of the sensitivity equations. A key feature is the reuse of information already computed for the state integration, hereby minimizing the extra effort required for sensitivity integration. Through case studies the new algorithm is compared to an extrapolation method and to the more established BDF based approaches. Several advantages of the new approach are demonstrated, especially when frequent discontinuities are present, which renders the new algorithm particularly suitable for dynamic optimization purposes.
Original languageEnglish
JournalComputers & Chemical Engineering
Volume28
Issue number12
Pages (from-to)2695-2707
ISSN0098-1354
DOIs
Publication statusPublished - 2004

Cite this

Kristensen, Morten Rode ; Jørgensen, John Bagterp ; Thomsen, Per Grove ; Jørgensen, Sten Bay. / An ESDIRK Method with Sensitivity Analysis Capabilities. In: Computers & Chemical Engineering. 2004 ; Vol. 28, No. 12. pp. 2695-2707.
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An ESDIRK Method with Sensitivity Analysis Capabilities. / Kristensen, Morten Rode; Jørgensen, John Bagterp; Thomsen, Per Grove; Jørgensen, Sten Bay.

In: Computers & Chemical Engineering, Vol. 28, No. 12, 2004, p. 2695-2707.

Research output: Contribution to journalJournal articleResearchpeer-review

TY - JOUR

T1 - An ESDIRK Method with Sensitivity Analysis Capabilities

AU - Kristensen, Morten Rode

AU - Jørgensen, John Bagterp

AU - Thomsen, Per Grove

AU - Jørgensen, Sten Bay

PY - 2004

Y1 - 2004

N2 - A new algorithm for numerical sensitivity analysis of ordinary differential equations (ODEs) is presented. The underlying ODE solver belongs to the Runge-Kutta family. The algorithm calculates sensitivities with respect to problem parameters and initial conditions, exploiting the special structure of the sensitivity equations. A key feature is the reuse of information already computed for the state integration, hereby minimizing the extra effort required for sensitivity integration. Through case studies the new algorithm is compared to an extrapolation method and to the more established BDF based approaches. Several advantages of the new approach are demonstrated, especially when frequent discontinuities are present, which renders the new algorithm particularly suitable for dynamic optimization purposes.

AB - A new algorithm for numerical sensitivity analysis of ordinary differential equations (ODEs) is presented. The underlying ODE solver belongs to the Runge-Kutta family. The algorithm calculates sensitivities with respect to problem parameters and initial conditions, exploiting the special structure of the sensitivity equations. A key feature is the reuse of information already computed for the state integration, hereby minimizing the extra effort required for sensitivity integration. Through case studies the new algorithm is compared to an extrapolation method and to the more established BDF based approaches. Several advantages of the new approach are demonstrated, especially when frequent discontinuities are present, which renders the new algorithm particularly suitable for dynamic optimization purposes.

U2 - 10.1016/j.compchemeng.2004.08.004

DO - 10.1016/j.compchemeng.2004.08.004

M3 - Journal article

VL - 28

SP - 2695

EP - 2707

JO - Computers & Chemical Engineering

JF - Computers & Chemical Engineering

SN - 0098-1354

IS - 12

ER -