# DENSERKS: Fortran sensitivity solvers using continuous, explicit Runge-Kutta schemes

2007) DENSERKS: Fortran sensitivity solvers using continuous, explicit Runge-Kutta schemes. Technical Report TR-07-34, Computer Science, Virginia Tech. (

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## Abstract

DENSERKS is a Fortran sensitivity equation solver package designed for integrating models whose evolution can be described by ordinary differential equations (ODEs). A salient feature of DENSERKS is its support for both forward and adjoint sensitivity analyses, with built-in integrators for both first and second order continuous adjoint models. The software implements explicit Runge-Kutta methods with adaptive timestepping and high-order dense output schemes for the forward and the tangent linear model trajectory interpolation. Implementations of six Runge-Kutta methods are provided, with orders of accuracy ranging from two to eight. This makes DENSERKS suitable for a wide range of practical applications. The use of dense output, a novel approach in adjoint sensitivity analysis solvers, allows for a high-order cost-effective interpolation. This is a necessary feature when solving adjoints of nonlinear systems using highly accurate Runge-Kutta methods (order five and above). To minimize memory requirements and make long-time integrations computationally efficient, DENSERKS implements a two-level checkpointing mechanism. The code is tested on a selection of problems illustrating first and second order sensitivity analysis with respect to initial model conditions. The resulting derivative information is also used in a gradient-based optimization algorithm to minimize cost functionals dependent on a given set of model parameters.

Item Type: | Departmental Technical Report |
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Keywords: | ODEs, Runge-Kutta methods, dense output, sensitivity analysis, tangent linear models, adjoint models, quadrature equations |

Subjects: | Computer Science > Mathematical Software |

ID Code: | 996 |

Deposited By: | Alexe, Mr. Mihai |

Deposited On: | 11 October 2007 |