Automatic differentiation of ODE integration
نویسنده
چکیده
3 Example: Differentiating the Lotka-Volterra ODE system 2 3.1 The Lotka-Volterra ODE system . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 3.2 The derivatives of the Lotka-Volterra ODE system . . . . . . . . . . . . . . . . . . 3 3.3 Integration of the original and augmented Lotka-Volterra ODE system with the Runge-Kutta method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
منابع مشابه
Automatic differentiation of numerical integration algorithms
Automatic differentiation (AD) is a technique for automatically augmenting computer programs with statements for the computation of derivatives. This article discusses the application of automatic differentiation to numerical integration algorithms for ordinary differential equations (ODEs), in particular, the ramifications of the fact that AD is applied not only to the solution of such an algo...
متن کاملOn the Solution of Some Inverse Problems in Infiltration
In this paper we discuss inverse problems in infiltration. We propose an efficient method for identification of model parameters, e.g., soil parameters for unsaturated porous media. Our concept is strongly based on the finite speed of propagation of the wetness front during the infiltration into a dry region. We determine the unknown parameters from the corresponding ODE system arising from the...
متن کاملOn Consistency Properties of Discrete Adjoint Linear Multistep Methods
In this paper we analyze the consistency properties of discrete adjoints of linear multistep methods. Discrete adjoints are very popular in optimization and control since they can be constructed automatically by reverse mode automatic differentiation. The consistency analysis reveals that the discrete linear multistep adjoints are, in general, inconsistent approximations of the adjoint ODE solu...
متن کاملUsing the Taylor Center to Teach ODEs
This article introduces a powerful ODE solver called the Taylor Center for PCs (http://www.ski.org/gofen/TaylorMethod.htm) as a tool for teaching and performing numeric experiments with ODEs. The Taylor Center is an All-in-One GUI-style application for integrating ODEs by applying the modern Taylor Method (Automatic Differentiation). The Taylor Center also offers dynamic graphics (including 3D ...
متن کاملAutomatic Diierentiation of Numerical Integration Algorithms
Automatic diierentiation (AD) is a technique for automatically augmenting computer programs with statements for the computation of derivatives. This article discusses the application of automatic diierentiation to numerical integration algorithms for ordinary diierential equations (ODEs), in particular, the ramiications of the fact that AD is applied not only to the solution of such an algorith...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- CoRR
دوره abs/1802.02247 شماره
صفحات -
تاریخ انتشار 2018