A Randomized Runge-Kutta Method for time-irregular delay differential equations
CoRR(2024)
摘要
In this paper we investigate the existence, uniqueness and approximation of
solutions of delay differential equations (DDEs) with the right-hand side
functions f=f(t,x,z) that are Lipschitz continuous with respect to x but
only Hölder continuous with respect to (t,z). We give a construction of the
randomized two-stage Runge-Kutta scheme for DDEs and investigate its upper
error bound in the L^p(Ω)-norm for p∈ [2,+∞). Finally, we
report on results of numerical experiments.
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