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Linear Stability Analysis of Runge-Kutta Methods for Singular Lane-Emden Equations
Journal of Nigerian Society of Physical Sciences, 2020 Runge-Kutta methods are efficient methods of computations in differential equations, the classical Runge-Kutta method of order 4 happens to be the most popular of these methods, and most times it is attached to the mind when Runge-Kutta methods are ...
M. O. Ogunniran +3 more
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Stochastic Runge–Kutta methods for multi-dimensional Itô stochastic differential algebraic equations
Results in Applied Mathematics, 2021 In this paper, we discuss the numerical solutions to index 1 stochastic differential algebraic equations. We introduce a new class of weak second-order stochastic Runge–Kutta methods for finding the numerical approximate solutions to multi-dimensional ...
Priya Nair, Anandaraman Rathinasamy
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Convergence of an Exponential Runge–Kutta Method for Non-smooth Initial Data
European Journal of Pure and Applied Mathematics, 2019 The paper presents error bounds for the second order exponential Runge-Kutta method for parabolic abstract linear time-dependent differential equations incorporating non-smooth initial data. As an example for this particular type of problems, the paper presents a spatial discretization of a partial integro-differential equation arising in financial ...
Gondal, Muhammad Asif +2 more
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Strong Stability Preserving Integrating Factor Runge-Kutta Methods [PDF]
SIAM Journal on Numerical Analysis, 2017 Strong stability preserving (SSP) Runge-Kutta methods are often desired when evolving in time problems that have two components that have very different time scales.
Leah Isherwood +2 more
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Extrapolated Implicit–Explicit Runge–Kutta Methods
Mathematical Modelling and Analysis, 2014 We investigate a new class of implicit–explicit singly diagonally implicit Runge–Kutta methods for ordinary differential equations with both non-stiff and stiff components. The approach is based on extrapolation of the stage values at the current step by
Angelamaria Cardone +3 more
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On strong stability of explicit Runge–Kutta methods for nonlinear semibounded operators [PDF]
IMA Journal of Numerical Analysis, 2018 Explicit Runge–Kutta methods are classical and widespread techniques in the numerical solution of ordinary differential equations (ODEs). Considering partial differential equations, spatial semidiscretizations can be used to obtain systems of ODEs that
Hendrik Ranocha
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Functional continuous Runge–Kutta–Nyström methods
Electronic Journal of Qualitative Theory of Differential Equations, 2016 Numerical methods for solving retarded functional differential equations of the second order with right-hand side independent of the function derivative are considered. The approach used by E. Nyström for second-order ordinary differential equations with
Alexey Eremin
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Strong approximation for Itô stochastic differential equations [PDF]
Iranian Journal of Numerical Analysis and Optimization, 2015 In this paper, a class of semi-implicit two-stage stochastic Runge-Kutta methods (SRKs) of strong global order one, with minimum principal error constants are given.
Mehran Namjoo
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A-stability preserving perturbation of Runge-Kutta methods for stochastic differential equations
Applied Mathematics Letters, 2020 The paper is focused on analyzing the linear stability properties of stochastic Runge–Kutta (SRK) methods interpreted as a stochastic perturbation of the corresponding deterministic Runge–Kutta methods.
V. Citro +2 more
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New class of hybrid explicit methods for numerical solution of optimal control problems [PDF]
Iranian Journal of Numerical Analysis and Optimization, 2021 Forward-backward sweep method (FBSM) is an indirect numerical method used for solving optimal control problems, in which the differential equation arising from this method is solved by the Pontryagin’s maximum principle.
M. Ebadi, I. Malih Maleki, A. Ebadian
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