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A Variable Stepsize Implementation for Stochastic Differential Equations [PDF]
SIAM Journal of Scientific Computing, 2003 Summary: Stochastic differential equations (SDEs) arise from physical systems where the parameters describing the system can only be estimated or are subject to noise. Much work has been done recently on developing higher order Runge--Kutta methods for solving SDEs numerically.
Kevin Burrage
exaly +7 more sources
Attractors under discretizations with variable stepsize
Discrete and Continuous Dynamical Systems, 2005 The authors investigate the attractors and study the upper and lower semi-continuity results for generalized discretizations with variable step size. They also discuss the convergence to the exact attractor in the Hausdorff metric space and the connections to pullback attractors in cocycle dynamics.
Barnabas M Garay, Keonhee Lee
exaly +2 more sources
Alexandria Engineering Journal, 2023 This article proposes a variable stepsize implementation of an improved one-step block method (OBM) that uses two intermediate points to solve Burgers' equation.
Mufutau Ajani Rufai, Bruno Carpentieri
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Variable stepsize SDIMSIMs for ordinary differential equations [PDF]
Applied Numerical Mathematics, 2021 Second derivative general linear methods (SGLMs) have been already implemented in a variable stepsize environment using Nordsieck technique. In this paper, we introduce variable stepsize SGLMs directly on nonuniform grid. By deriving the order conditions of the proposed methods of order $p$ and stage order $q=p$, some explicit examples of these methods
Arash Jalilian +2 more
openaire +2 more sources
Second derivative General Linear Method in Nordsieck form
Journal of Numerical Analysis and Approximation Theory, 2019 This paper considers the construction of second derivative general linear methods (SD-GLM) from hybrid LMM and their transformation to Nordsieck GLM. How the Runge-Kutta starters for the methods can be derived are given.
Robert I. Okuonghae +1 more
doaj +7 more sources
Fractal and Fractional, 2023 This paper presents a new hybrid block method formulated in variable stepsize mode to solve some first-order initial value problems of ODEs and time-dependent partial differential equations in applied sciences and engineering.
Mufutau Ajani Rufai +2 more
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Variable stepsize construction of a two-step optimized hybrid block method with relative stability
Open Physics, 2022 Several numerical techniques for solving initial value problems arise in physical and natural sciences. In many cases, these problems require numerical treatment to achieve the required solution.
Baleanu Dumitru +3 more
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Some efficient Nordsieck integration methods for IVPs [PDF]
Iranian Journal of Numerical Analysis and Optimization, 2018 In this paper, in continuation of the construction of efficient numerical methods for stiff IVPs, we construct type two Nordsieck second derivative general linear methods with order p = s, where s is the number of internal stages, and stage order q = p ...
N. Barghi Oskouie, A. Abdi, G. Hojjati
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Fractal and Fractional, 2023 The fractional gradient method has garnered significant attention from researchers. The common view regarding fractional-order gradient methods is that they have a faster convergence rate compared to classical gradient methods.
Luotang Ye, Yanmao Chen, Qixian Liu
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Energies, 2020 This manuscript aims to incorporate an inertial scheme with Popov’s subgradient extragradient method to solve equilibrium problems that involve two different classes of bifunction.
Habib ur Rehman +4 more
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