An explicit trigonometrically fitted Runge–Kutta method for stiff and oscillatory problems with two frequencies
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DOI: 10.1080/00207160.2018.1437263
Abstract: ABSTRACT In this paper, a new explicit fourth-order Runge–Kutta method adapted to oscillatory problems with two frequencies (μ and ν) is developed. The new method can integrate exactly the different harmonic oscillators and simultaneously. Numerical… read more here.
Keywords: problems two; kutta method; two frequencies; method ... See more keywords
Development and Application of an Exponential Method for Integrating Stiff Systems Based on the Classical Runge–Kutta Method
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DOI: 10.1134/s0012266118070066
Abstract: We study numerical methods for solving stiff systems of ordinary differential equations. We propose an exponential computational algorithm which is constructed by using an exponential change of variables based on the classical Runge–Kutta method of… read more here.
Keywords: classical runge; kutta method; method; stiff systems ... See more keywords
Explicit order 3/2 Runge-Kutta method for numerical solutions of stochastic differential equations by using Itô-Taylor expansion
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DOI: 10.1515/math-2019-0124
Abstract: Abstract This paper aims to present a new pathwise approximation method, which gives approximate solutions of order 32 $\begin{array}{} \displaystyle \frac{3}{2} \end{array}$ for stochastic differential equations (SDEs) driven by multidimensional Brownian motions. The new method,… read more here.
Keywords: expansion; kutta method; method; stochastic differential ... See more keywords