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A numerical approach based on Pell polynomial for solving stochastic fractional differential equations
In this article, Pell operational matrix method is discussed to solve the stochastic fractional differential equation. For that purpose, the Pell...
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Enhanced moving least squares method for solving the stochastic fractional Volterra integro-differential equations of Hammerstein type
One of the challenging and practical issues that have recently attracted the attention of researchers is stochastic equations. One of the important...
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Convergence and stability of the Milstein scheme for stochastic differential equations with piecewise continuous arguments
This work develops the Milstein scheme for commutative stochastic differential equations with piecewise continuous arguments (SDEPCAs), which can be...
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Convergence rate and exponential stability of backward Euler method for neutral stochastic delay differential equations under generalized monotonicity conditions
This work focuses on the numerical approximations of neutral stochastic delay differential equations with their drift and diffusion coefficients...
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Strong convergence of explicit numerical schemes for stochastic differential equations with piecewise continuous arguments
In 2015, Mao (J. Comput. Appl. Math., 290, 370–384, 2015) proposed the truncated Euler-Maruyama (EM) method for stochastic differential equations...
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The truncated Euler-Maruyama method for highly nonlinear stochastic differential equations with multiple time delays
The main aim of this paper is to investigate the strong convergence order for the truncated Euler-Maruyama (TEM) method to solve stochastic...
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An Analysis of Universal Differential Equations for Data-Driven Discovery of Ordinary Differential Equations
In the last decade, the scientific community has devolved its attention to the deployment of data-driven approaches in scientific research to provide...
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Price prediction and selling strategy optimization using the Feynman formula differential equations
In the field of e-business, strategic pricing, and competent inventory management are crucial for commerce sustainability. This study explores the...
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Considering Multiplicative Noise in a Software Reliability Growth Model Using Stochastic Differential Equation Approach
A Software reliability growth models are very useful to investigate software reliability characteristics quantitatively and to establish relationship...
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Accurate and stable numerical method based on the Floater-Hormann interpolation for stochastic Itô-Volterra integral equations
In various fields of science and engineering, such as financial mathematics, mathematical physics models, and radiation transfer, stochastic integral...
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Inherently interpretable machine learning solutions to differential equations
A machine learning method for the discovery of analytic solutions to differential equations is assessed. The method utilizes an inherently...
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An efficient meshless method to approximate semi-linear stochastic evolution equations
In this article, we are concerned with meshless methods to approximate and simulate the solution of semi-linear stochastic evolution equations. We...
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A survey of mean-square destabilization of multidimensional linear stochastic differential systems with non-normal drift
Mean-square stability analysis of linear stochastic differential systems obtained perturbing ordinary systems by linear terms driven by independent...
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Moment Evolution Equations and Moment Matching for Stochastic Image EPDiff
Models of stochastic image deformation allow study of time-continuous stochastic effects transforming images by deforming the image domain....
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Solving partial differential equations using large-data models: a literature review
Mathematics lies at the heart of engineering science and is very important for capturing and modeling of diverse processes. These processes may be...
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Attentive neural controlled differential equations for time-series classification and forecasting
Neural networks inspired by differential equations have proliferated for the past several years, of which neural ordinary differential equations...
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Using a library of chemical reactions to fit systems of ordinary differential equations to agent-based models: a machine learning approach
In this paper, we introduce a new method based on a library of chemical reactions for constructing a system of ordinary differential equations from...
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Ordinary Differential Equations
A differential equation is an equation that contains a function and one or more of its derivatives. They have been studied ever since the invention...
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Bayesian parameter inference for partially observed stochastic volterra equations
In this article we consider Bayesian parameter inference for a type of partially observed stochastic Volterra equation (SVE). SVEs are found in many...
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Efficient Solution of Stochastic Galerkin Matrix Equations via Reduced Basis and Tensor Train Approximation
This contribution focuses on the development of a computational method to efficiently solve matrix equations arising from stochastic Galerkin (SG)...