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Enabling New Flexibility in the SUNDIALS Suite of Nonlinear and Differential/Algebraic Equation Solvers [PDF]
ACM Transactions on Mathematical Software, 2020 In recent years, the SUite of Nonlinear and DIfferential/ALgebraic equation Solvers (SUNDIALS) has been redesigned to better enable the use of application-specific and third-party algebraic solvers and data structures.
D. J. Gardner +3 more
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Rossler’s system using piecewise derivative
Results in Physics, 2023 This article deals with a piecewise system named piecewise Rossler’s system which exhibits a concept of piecewise derivatives based on Classical-power-law randomness, Classical Mittag-Leffler-law-randomness, and Classical fading memory randomness ...
Atul Kumar
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Min-max differential game with partial differential equation
AIMS Mathematics, 2022 In this paper, we are concerned with a min-max differential game with Cauchy initial value problem (CIVP) as the state trajectory for the differential game, we studied the analytical solution and the approximate solution by using Picard method (PM) of ...
Ebrahim. A. Youness +3 more
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Growth of Solutions of Homogeneous Differential–Difference Equations
Computer Sciences & Mathematics Forum, 2023 In this article, we study the growth properties of solutions of homogeneous linear differential–difference equations in the whole complex plane ∑j=0nAjzfjz+cj=0, n∈N+, where cj, j=0,...,n are complex numbers, and Aj(z), j=0, …, n are entire functions of ...
Hakima Lassal, Benharrat Belaϊdi
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Differential inequality and non-oscillation of fourth order differential equation [PDF]
Қарағанды университетінің хабаршысы. Математика сериясы, 2021 The oscillatory theory of fourth order differential equations has not yet been developed well enough. The results are known only for the case when the coefficients of differential equations are power functions.
A.A. Kalybay, A.O. Baiarystanov
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AIMS Mathematics, 2022 The basic objective of this paper is to utilize the factorization technique method to derive several properties such as, shift operators, recurrence relation, differential, integro-differential, partial differential expressions for Gould-Hopper-Frobenius-
Rabab Alyusof , Mdi Begum Jeelani
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Graph Neural Controlled Differential Equations for Traffic Forecasting [PDF]
AAAI Conference on Artificial Intelligence, 2021 Traffic forecasting is one of the most popular spatio-temporal tasks in the field of machine learning. A prevalent approach in the field is to combine graph convolutional networks and recurrent neural networks for the spatio-temporal processing.
Jeongwhan Choi +3 more
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Tikrit Journal of Pure Science, 2021 The aim of this paper is to study It ’s formula for some stochastic differential equation such as quotient stochastic differential equation, by using the function F (t, x (t)) which satisfies the product Ito’s formula, then we find some calculus ...
Abdulghafoor J. Salim, Ali F. Ali
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A Comparison of Automatic Differentiation and Continuous Sensitivity Analysis for Derivatives of Differential Equation Solutions [PDF]
IEEE Conference on High Performance Extreme Computing, 2018 Derivatives of differential equation solutions are commonly for parameter estimation, fitting neural differential equations, and as model diagnostics. However, with a litany of choices and a Cartesian product of potential methods, it can be difficult for
Christopher Rackauckas +7 more
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A Universal Ordinary Differential Equation [PDF]
Logical Methods in Computer Science, 2020 An astonishing fact was established by Lee A. Rubel (1981): there exists a fixed non-trivial fourth-order polynomial differential algebraic equation (DAE) such that for any positive continuous function $\varphi$ on the reals, and for any positive ...
Olivier Bournez, Amaury Pouly
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