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On the Complexity of Parametric ODEs and Related Problems

  • Stefan HeinrichEmail author
Chapter

Abstract

We present an iterative Monte Carlo procedure to solve initial value problems for systems of ordinary differential equations depending on a parameter. It is based on a multilevel Monte Carlo algorithm for parametric indefinite integration. As an application, we also obtain a respective method for solving almost linear first order partial differential equations. We also consider deterministic algorithms.

We study the convergence and, in the framework of information-based complexity, the minimal errors and show that the developed algorithms are of optimal order (in some limit cases up to logarithmic factors). In this way we extend recent complexity results on parametric ordinary differential equations. Moreover, we obtain the complexity of almost linear first-order partial differential equations, which has not been analyzed before.

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Computer ScienceUniversity of KaiserslauternKaiserslauternGermany

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