Related DatabasesWeb of Science You must be logged in with an active subscription to view this.Article DataHistorySubmitted: 23 February 2021Accepted: 25 October 2021Published online: 18 January 2022Keywordssensitivity analysis, adjoint, PETSc, second-order adjointAMS Subject Headings97N80, 65L99, 49Q12Publication DataISSN (print): 1064-8275ISSN (online): 1095-7197Publisher: Society for Industr...

3. The Implicit Function Theorem and its special case, the Inverse Function Theorem. Relation to the Contraction Mapping Fixed Point Theorem. Computation of several iterates of the approximating sequence to the implicit function. Continuity and differentiability of the implicit function. Application to differentiable variation of the fixed point in the Contraction Mapping Fixed Point Theorem. 4...

Applied scientists often like to use ordinary differential equations (ODEs) to model complex dynamic processes that arise in biology, engineering, medicine, and many other areas. It is interesting but challenging to estimate ODE parameters from noisy data, especially when the data have some outliers. We propose a robust method to address this problem. The dynamic process is represented with a n...

In this paper, we develop a family of second-order semi-implicit time integration methods for systems of ordinary differential equations (ODEs) with stiff damping term. The important feature of the new methods resides in the fact that they are capable of exactly preserving the steady states as well as maintaining the sign of the computed solution under the time step restriction determined by th...

The paper deals with stiff systems of differential equations. To solve this sort of system numerically is a diffult task. In spite of the fact that we come across stiff systems quite often in the common practice, a very interesting and promissing numerical method of solving systems of ordinary differential equations (ODE) based on Taylor series has appeared. The question was how to harness the ...

Obtaining the transient probability distribution vector of a continuous-time Markov chain (CTMC) using an implicit ordinary differential equation (ODE) solver tends to be advantageous in terms of run-time computational cost when the product of the maximum output rate of the CTMC and the largest time of interest is large. In this paper, we show that when applied to the transient analysis of CTMC...

The derivation of 5th order diagonal implicit type Runge Kutta methods (DITRKM5) for solving 3rd special ordinary differential equations (ODEs) is introduced in the present study. DITRKM5 techniques are name approach. This approach has three equivalent non-zero elements. To investigate current study, a variety tests five various initial value problems (IVPs) with different step sizes h were imp...